So Japan in particular has a very interesting perspective towards religion in video games and it shows up in a lot of their works.
http://www.escapistmagazine.com/articles/view/issues/issue_280/8316-The-Devil-Went-Down-to-Nippon
A lot of the Final Fantasy games have religions that tend to be portrayed very negatively as institutional power houses, lying and manipulating the populace, very intolerant (and often working with very devilish powers). In FFX Wakka was a simple but devote person betrayed by the religious figures who led him astray. It will always been a false religion stealing life force from the earth, or crystals etc to gain power, even that or aligning with an actual vengeful deity that the player has to then kill off. FFX, FFXII
Bayonnetta does the standard 'Angels are really the bad guys' sort of plotline and is clearly taking a lot from catholic imagery and even
This happens in Shi Megamai Tensei too.
And then you've got games like Okami which are built around very rich artistic mythical religions, but don't seem to focus much on the practitioners themselves and are very fable like. Lots of Crystal Dragon Jesus too.
http://tvtropes.org/pmwiki/pmwiki.php/Main/CrystalDragonJesus
There's the 'God games' Black&White, Populus whose mechanics portray Gods manipulating the world as they see fit to their whims, with a focus on the manipulation over a cohesive philosophy or idea.
There's Bioshock Infinite with it's fairly anti-religion stance. (Although that was toned down a lot from what it was originally going to be apparently. A developer at irrational decided he couldn't make the game anymore and wanted to resign and Ken Levine sat down and talked to him and realised there was a whole side of the story he'd never even thought about because he'd never grown up in a particularly religious environment).
I'd though of another western game, but I'm afraid it's slipped my mind.
...I'm not sure if any of these games have ever done religion particularly well. A lot of it's surface level imagery and I can't say I've ever been moved in either way by most of these games. It's rarely tied in mechanically and they normally don't focus on the personal experiences, good or bad. Generally games seem to be fairly hostile and one of the things that shocked me most was that in Mass Effect 1 the game actually allowed you to choose if you wanted to be religious or not. That was pretty amazing and made me a lot more attached to the PC than I thought I would be.
But it shows the state of games, that the idea that you could have a choice or even that the main character would have a religion was a huge surprise to me. Most games dodge the question for fear of alienating the fan base.
Shepard is a good example of a character that reaches godhood too. More and more revolves around her and she has her own myth and legend of the universe-protector steadily ramping up through the games until she almost does reach practically godhood with the control option. Her position of arbiter of the way the universe will go feels very deistic and she literally
rises to that in the end of the game.
Equally I think Revan reaches a deistic level in KotoR canon. There's something about the PC having the power to change the fate of the universe that does it.
Sephiroth is a non PC who reaches demonhood/godhood. His final battle song is called 'One-winged Angel' for a reason
I'm quite interested in that idea and I'll keep on thinking about characters that do that
EDIT: I forgot the Left Behind games! It's hard to judge how effective the games were, because the people behind the Left Behind series have a crazy 'I can't wait till all the heretics' die backwards set of beliefs so divorced from reality that in their novels they have nurses say lines like 'It's a shame all the babies are gone because now we can't have any more abortions'
In that respect a game where you can mechanically kill unbelievers and then regain everything lost by saying a quick prayer perfectly represents the crazyness of it's makers and their beliefs, but it's not a game I'd ever want anyone to play