From Battlestar Wiki, the free, open content Battlestar Galactica encyclopedia and episode guide
One of the Number Ones, prior to being discovered among the Fleet, posed as Brother Cavil, a member of the Colonial clergy. However, contrary to his assumed role, he did not share the other Cylons' religious beliefs and frequently mocked them.
"John" and the Final Five
After the Final Five contacted the Centurions, they agreed to create humanoid Cylons and share resurrection technology with them in exchange for an end to the Cylon War. The first humanoid Cylon created by the Final Five was "John", named after and created in the likeness of Ellen Tigh's biological father. He was "treasured" by the Five, and even assisted them in the creation of the other seven models (TRS: "No Exit").
John grew intensely jealous of Daniel, the seventh model, because Daniel was emotionally favored by Ellen. John sabotaged the Sevens' genetic code and amniotic fluid, wiping out the entire line permanently.
He later trapped the Final Five in a room, suffocated them, and boxed them before they could be resurrected fully. Eventually, he resurrected them one at a time but obscured their original memories, gave them false ones, and planted each of them "like a Boomer" among the humans in an effort to teach them a lesson about their foolish appreciation for humans. This plan backfires when The Five become even more sympathetic towards the Colonials, a fate that is eventually sealed with the destruction of the Resurrection Hub. Without The Hub, The Five can no longer regain their original memories, thus remaining Colonials and enemies with John. Although The Five still unconsciously possess their lost memories, if any of The Five were to die then the knowledge needed to recreate resurrection technology would be lost forever.
John also corrupted the memories of his six surviving "sibling" models to remove from them the knowledge of the Final Five's identities and programmed them not to think about the matter, though they still knew that another five models were extant. John pretended to know no more about the Five than his fellows did, insisting that the imperative not to seek them out came from the "original programmers" (TRS: "Six of One"). John was extremely contemptuous of many of the human traits the Five gave him. He eliminated his need for sleep and dreaming by rewriting his own software, having previously suffered from night sweats and dreams in which he was being pursued through yellow mists by dog-faced boys.
This copy is first seen on a Resurrection Ship with another copy (possibly the Caprica copy) looking at the empty new bodies of the Final Five. The two believe that the Five will be killed in the Colonies destruction and will download and apologize. This Cavil decides to go and be with Ellen when it happens. He encounters her in a bar on Picon and is upset to realize that she hasn't changed. When she asks for his name, he refuses to give it to her saying that he's just a mysterious stranger. When the attack happens, Cavil huddles with Ellen and while both survive the nuclear blast, Ellen is severly hurt. Cavil decides to keep her alive as she hasn't learned her lesson and escorts her to the Rising Star. There he sits beside her bed as the Cylons chase and attack the Fleet every 33 minutes and muses on how four of the Five are in the Fleet but Anders isn't. Cavil admits that keeping her alive like this is cruel but shows no remorse.
Cavil later installs himself as a clergyman on Galactica and hands out pamphlets about "the plan" to lure any other Cylons to him. He ends up with two Sixes (one being Shelly Godfrey), a Two and a Five and is disappointed that there are no Threes or Fours, although Godfrey claims to have seen a Four in the Fleet. Cavil assumes leadership of the group and takes control of their sleeper agent. Cavil's group repeatedly fails and he is forced at one point to airlock Shelly Godfrey and is pissed that Boomer failed to kill Adama. This copy also deals with a young boy named John who is unwanted by his parents and takes a likeing to Cavil after running into him in a corridor. Cavil initally rebuffs him, but apparently grows either somewhat sympathetic to, or intrigued by, him and lets him into his chapel and feeds him. Cavil takes care of John for an unknown amount of time, but after finally learning John's name and that John considers them friends, Cavil murders him saying "friends are a dangerous thing to have" and shows no remorse for it (TRS: "The Plan").
On Galactica, Cavil provides counsel for Chief Tyrol after Tyrol's maddened attack against Cally Henderson. Cavil identifies the source of Tyrol's anxiety as arising from the fear that he could be a Cylon sleeper agent. This Cavil seems to be personally very familiar with Tyrol and is apparently aware that Henderson harbors romantic feelings for him (TRS: "Lay Down Your Burdens, Part I"). (Later analysis of Cavil's nature, from behavior in season 3 and 4 episodes, suggests that Cavil's comments were aimed to incite torment in Tyrol.)
A somewhat eccentric figure, Cavil is a surprisingly harsh critic of prayer for a Brother, but claims to have been preaching "longer than you [Tyrol] have been sucking down oxygen" (TRS: "Lay Down Your Burdens, Part I"). 
Despite his cynicism, Cavil prays with Laura Roslin for her re-election to the presidency to be successful. When Tyrol deduces the Caprica copy of him as a Cylon, Cavil is thrown in the brig along with his copy claiming right up until he sees the Caprica copy that he isn't a Cylon at which time he drops the act. He is later ejected through an airlock along with his copy. On the way to his execution, he finds himself in a corridor surrounded by the unknowing Final Five and muses for a moment on the irony of the situation. When asked by his copy if there's a Resurrection Ship waiting for them, he confirms that and is disgusted with his copy's change of mind about humanity and plans to have him boxed. Cavil reveals once he resurrects he plans to start the complete destruction of humanity and holds hands with his copy as they're blown out into space through the launch tube by Admiral Adama himself (TRS: "Lay Down Your Burdens, Part II, The Plan").
A copy of this model infiltrates Samuel Anders' resistance group on Caprica and uses his cover as a priest to ingratiate himself directly with Anders. He co-ordinates with a Number Four copy who is posing as the team doctor for the Caprica Buccaneers and undermines the resistance's morale. During his time with the resistance he counsels Anders and listens to his confessions of self-doubt and cowardice. He also learns of Anders' love for his human companions and for the people he has lost and slowly comes to the realization that the Cylons' attack on the Colonies was a grave error, as the Final Five would continue to love humanity and mourn them even if they were extinct. This is reinforced when Cavil is presented with an opportunity to kill Kara Thrace and Anders, but instead shows them mercy and allows them to reunite. Cavil comes to regret the actions of the Cylons and expresses his relief when a Number Six arrives shortly after Thrace's SAR landing and informs him of the new truce between Cylon and man, despite also being informed that his model voted against it. He decides to go to Galactica and act as the envoy of the truce, telling them that the Cylons had left the Colonies. Upon his arrival aboard Galactica he is identified as a Cylon by Chief Tyrol and detained. Cavil admits to being a Cylon and says "take me to your leader" (TRS: "The Plan").
Due to this copy's discovery, the Fleet copy is arrested as well and thrown in Galactica's brig. Caprica-Cavil informs President Roslin and Admiral Adama that the Cylons have realized that they made two mistakes: the attack on the Colonies and the pursuit of the Fleet, so both the occupation of the Colonies and the Cylon pursuit of the humans are now over. After receiving the message, Roslin orders that both Cavils be airlocked (TRS: "Lay Down Your Burdens, Part II").
Like his Fleet counterpart, the Caprica copy also expresses doubt in the active involvement of divine forces in the real world, although he focuses his contempt on the Cylon religion. He says that "There is no God", something that the Ones have been telling the other Cylons for years, though he acknowledges that God's existence or nonexistence can't actually be proven. Based on his conversation with the Fleet copy, this viewpoint appears to be shared across the entire model.
While in the airlock awaiting execution, this Cavil engages in a debate with Galactica's Cavil regarding his epiphany. He tries to enlighten his more cynical brother to his revelation, but is rebuked and scorned. The Galactica Cavil promises to have him boxed for his radical heresy, yet still takes his hand when he offers it seconds before being flushed into the void. While the Galactica Cavil closes his eyes, this copy does not and meets his fate with eyes wide open (TRS: "The Plan"). If he did download and get boxed, his conciousness was presumably destroyed when the Resurrection Hub was destroyed. (TRS: "The Hub")
New Caprica Copies
At least two Ones are present in the invasion fleet on New Caprica (TRS: "Occupation", "Precipice"). They have some authority over humans in detention, as Ellen Tigh is able to use sexual favors to bribe another into releasing Saul Tigh. This was a self-serving ruse; after a second sexual encounter, a One admits to Ellen that Saul was released in order to give the Cylon authorities a way of tracking and putting down the New Caprica Resistance (TRS: "Precipice").
It turns out that these liasons were highly Oedipal in nature. Not only does was Cavil modeled after Ellen's father, he is technically her "son", though only Cavil knew the extent of their relationship at the time. Though he appears to have no qualms about it when it happens, Ellen later makes a pointed reference to it, using it as a barb to belittle Cavil and he expresses a tactful amount of shame and frustration about it (TRS: "No Exit").
Two copies are also involved in the Cylon leaders' discussions, such as whether to kill Gaius Baltar.
Another copy also acts as a type of liaison between the NCP and their Cylon masters. He gives Jammer the list of Colonials to detain, and later accompanies the NCP to the site of a mass execution of Colonial detainees (TRS: "Occupation").
The NCP liaison version is critically wounded during an attack by the Resistance movement. One is left with a bullet wound to the stomach and is left to die after the detainees are liberated. He resorts to suicide by severing his carotid artery with a spent casing. He downloads into a new body for the third time; an experience that, as he explains, is similar to having a white hot poker slammed through his skull (TRS: "Exodus, Part I").
Basestar Command Copies
After the Cylon fleet arrives at the algae planet, a Cylon negotiation team negotiates a meeting on Galactica, which consists of Gaius Baltar, Boomer, a Number Three, and a Number One. The One ad-libs during the discussion, personally suggesting that the Cylons will hand over Baltar to the Colonials as part of the negotiation ("to sweeten the pot").
Later, a One (likely the same one) argues that they should destroy Galactica now and be rid of them for good. He thinks it does not matter if the Cylons find Earth in five days or five thousand years, saying that they can last forever, whereas the Colonials cannot. He concludes that Admiral Adama's threat to launch nuclear weapons at the temple is a bluff, even as Galactica prepares its missile launchers. After Adama fails to back down, One agrees to the consensus to recall the Heavy Raiders and is angry when all but one returns, saying that they have to "do something" about the Threes and their defiance (TRS: "The Eye of Jupiter, Rapture").
A copy accompanies D'Anna Biers and Baltar to the Temple of Five to look for clues on Earth's location. He helps disarm the G-4 detonators and becomes angry when Biers wants to find out the identities of the Final Five, insisting that it is forbidden. When Biers does not relent, Cavil points a gun at her, but before he can shoot, Baltar kills him from behind with an abandoned Colonial pistol. (TRS: "Rapture")
Another copy greets Number Three when she resurrects on a Resurrection Ship and informs her of the decision to box her model. She replies that someday he will know the truth of the Final Five like she does just before he removes the device storing her consciousness. Other Cavils are shown boxing other Number Threes all over the room in the Resurrection Ship (TRS: "Rapture").
Faction Leader Copy
In "Six of One" a Number One model, consistently referred to as "Cavil", despite the egalitarian and democratic principles of Cylon command, exudes an definite sense of assumed authority. As of such, he appears to be the de facto leader of one side of the schism between the Cylons, composed of Ones, Fours, Fives, and Sharon Valerii, opposed to the Twos, Sixes and Eights loyal to Natalie. His is among the first blood shed in the Cylon Civil War, as Natalie has the self-aware Centurions (a concept Cavil is horrified by) attack. He initially appears to be forgiving, negotiating generous terms of truce with the rebels, although this is turns out to be a ploy for a devastating ambush, one which he justifies: "they started it".
Cavil is in a sexual relationship with Valerii, although the nature of it is odd, he condescendingly refers to her as his "pet Eight" (TRS: "The Hub"). He has been holding Ellen Tigh prisoner ever since she was killed by her husband and resurrected (TRS: "No Exit").
This copy is killed by Number Three after he un-boxes her to try to convince her to get the rebels to stop. She breaks his neck when she learns of the attack on the Hub, believing that he won't have time to resurrect before it is destroyed (TRS: "The Hub").
It is likely that she was wrong, as Boomer brings a kidnapped Hera to a Number One which seems to be the same Cavil. He may have had to time to resurrect before the Hub was destroyed contrary to what D'Anna thought. It is equally possible that this is a different copy entirely, as they seem to share similar personalities. Regardless, this copy, alongside a Simon, runs many tests on the child. (TRS: "Islanded in a Stream of Stars").
During the attack on The Colony, Cavil invades the Galactica CIC to take back Hera Agathon. He agrees to hand her over to the Colonials in exchange for the secret of Resurrection, and backs down. His trademark sarcasm surfaces when he is impatient with the Final Five, saying they're "keeping two civilizations waiting". When Tyrol attacks and kills Tory Foster, he takes this as a sign of aggression, attacking the Colonials. When his attack fails, he swears and puts a gun in his mouth, committing suicide. Many other Number One copies died with him when The Colony falls into the black hole it was orbiting and is destroyed. (TRS: "Daybreak, Part II")
In "Occupation" and "Precipice", the Ones are the most outwardly sadistic and cruel to humans, appearing to take pleasure (or at least a noticeable level of amusement) in their own acts of psychological and physical cruelty. They are even described by one of their creators, Ellen Tigh, as being sadists. The Ones like toying with the idea of liquidating the human population on New Caprica as a solution to the Resistance, to "perhaps a more manageable number. Say, less than a thousand."
The Ones are described as being driven by base emotions, principally anger and jealousy (TRS: "No Exit"). They try to hide behind a facade of genial yet sarcastic superiority, but when situations move beyond their control they often lash out in rage, abandoning any pretense of civility. The Ones are a vindictive model; even their creators do not escape their anger and wrath. They specifically torture the Final Five psychologically and physically as a means of exacting "justice" for perceived slights against them. In conversation with the other Cylons, Ones are vocal and callous proponents of harsh measures against the New Caprica Resistance and are strong advocates of mass executions.
Though apparently atheistic, the first two known copies of this model pose as clergy, possibly as an intentional mockery of religion on their part. The Cavils on New Caprica often speak of "God" sarcastically when among other Cylons but seem to recognize the pragmatic aspects of religion, referring to the Cylon "plan" as "God's Plan." The Cavil who lead the main Cylon faction against the rebel faction is also implied to possess more personal knowledge than other Cylons as the nature of the Cylon god and possibly the Final Five. He plays a "gatekeeper" role, and refers to "God" as "the voice of reason."
With the Cylons apparently occupying New Caprica at the end of the Lay Down Your Burdens, Part II, it appears that the Ones on Galactica are either lying about the Cylon change of heart or the Cylon plans changed after the second Number One was captured on Galactica.
"Exodus, Part I" reveals that a Number One unit, the leader of the execution squad intercepted by the Resistance and who died there (his third death), experienced increasing head pain with each resurrection.
Several comments Number One makes in the episode "The Ties That Bind" indicate that he has some deeper knowledge of the Centurions than the rest of the Cylons do. This is because the Ones are the eldest of the eight Colonial-era humanoid Cylons, the first to be created by the Final Five. They played a key role in helping the Five create both their seven brother and sister models and the advanced Centurions and Raiders.
Given his conversations with Ellen Tigh in "No Exit" and his reaction to the defiance of the Threes, it seems that Cavil is the driving force behind the boxing of the Threes. While he claims to them--and presumably to the other Cylon models--that it needed to be done in response to their rejection of the consensus command of the Cylons, it is clearly an effort to keep the identities of the Final Five from being exposed.