The term belief system referred to any set of mutually supportive beliefs that might underly the actions of individuals in a certain culture.
Many ritualistic cultures incorporated the idea of balance into their belief systems. The D'Arsay civilization appeared to be an example. (TNG: "Masks")
The Novan culture was built on the belief that Humans attacked their ancestors and sent them the "poison rain". (ENT: "Terra Nova")
Captain Kathryn Janeway believed there was a limit to the religious practiced on USS Voyager, clarifying that if their belief system required a crewmen to sacrifice a child to their gods, she would not allow it. (VOY: "Barge of the Dead")
Due to the odd passage of time on Kelemane's planet, Voyager was visible over the planet for hundreds of years, embedding itself in the inhabitants belief system. (VOY: "Blink of an Eye")