There's three ways I've noticed religion in games. The first two are the way I've seen it done in the vast majority of games though.
1) Being used as an easy reference point. People already know the basics of these gods/religious figures. So when we use them, people already recognize aspects of them. When you name a character "Thor" your first thought as a player is generally "Oh, they are the God of Thunder." (Depending on the game/setting. Contextually they might just be someone who shoots lightning or whatever). For example, God of War. We already knew the relationship between a lot of the Gods/characters etc. without having to spend a lot of time saying things. There was also chances for them to give nods to aspects etc. (I'm mostly talking about the first God of War).
Final Fantasy again... Does this a lot. Religions of their own creation still count sort of, however in every game I've seen (or can remember) of theirs, religion = bad.
I disagree. In FF X, the main religion isn't necessarily "bad", but it is made clear that it isn't the be-all and end-all and it has its downsides as well as its merits (being the straw of hope in a tormented world) and X-2 briefly explored what happens when a major belief is lost/abandoned.
Thank you for the responses regarding paganism in the lore of games.
Good point. The paganism of most modern games is from the western world and - in particular - the Greco-Roman pantheons.
I believe one of the reasons we use (and tend to overlook) pagan lore is that it's so common in our society - probably more common than most of the aspects of monotheism, although most of us are taught to try to fit the pagan stuff into a monotheistic cosmos. Most of us have grown up with stories and customs - and games - that present pagan themes. I think there is a historical precedent for this, actually. There was a time - typified by events like the Council of Nicea and ideas like the Arian heresy - when many pagan ideals and archetypes were necessary but vilified. Instead of being lost entirely, they were encoded in things like fairy tales or holiday trappings. They hid as things so ludicrous that no serious (monotheistic) person took them as a threat.
Umm, i don't know if this series was mentioned but... Shin Megami Tensei. The original series, the first on the Nintendo up into post SNES was a very religion heavy game. I mean, in number 2 you can actually fight to defeat Yahweh(Hebrew name for God). It has the other dieties of religions and explains them as demons who choose to oppose the will of an all oppressive godlike being who tries to decide the fate of others.