English, or some language that is universally translated into it (à la Tolkien) is standard. Loanwords from foreign languages ("fascist", "karma", etc.) occur with normal frequency, as do chronologically enigmatic borrowings such as the Battlestar Columbia. Most religious terms are explicitly shared with ancient greek beliefs (either antecedent to or descendent from them).
Accents
Most characters speak with a standard american accent, with some exceptions.
English Accent
Two characters speak with an accent resembling received pronunciation, Dr. Gaius Baltar of Caprica and ship's medic Ishay. Other characters from Caprica do not share this accent.
Spanish Accent
A woman rescued from Caprica by Sharon Valerii spoke with a spanish or portugese accent, and inquired after the whereabouts of her husband, who she stated was "stationed on Geminon". Her place of origin is unclear, but no other characters from either Caprica, Gemenon, or anywhere else have shared this accent.
Aerelon Accent
In the episode "Flesh and Bone", Baltar noted that Sharon Valerii spoke with a trace of an Aerelon accent. The actress who portrays her, Grace Park, speaks English with a standard american accent, but is also fluent in Korean.