Does Bible-Man count? :P

Inquisitor might be what you're looking for.

It's not a part of the gameplay, exactly, but Driftmoon has some Christianity / Bible references sprinkled here and there in books / scrolls that you can find and read.

Oh, buy Driftmoon. Really nice game.

Loved it for years.

Heresy! They have Call of Cthulhu "Prisoner of Ice" and "Shadow of the Comet"... or were you thinking of a different one?

-- Axys Adventures – Truthseeker
-- Forgiveness

Apotheon is both an awesome game and heavily features ancient greek gods (so far I've fought quite a few of them) so might fit the bill.

Not on GoG, but Age of Mythology deals with Norse, Greek and Egyptian mythology and religion.

Can't really think of any with more contemporary religions... I imagine that's a can of worms not many developers are willing to open...

He was faster than me. I second that. It has a nice mix of jewish apocrypha (13 clans, the lilith figure, kabalistic sorcery), real world superstition (gypsy woman selling charms and "seeing" things for instance) plus real reference to historic sects and major religions (pagan barbarians, knights of st john, teutonic order, christianity, crusades/crusaders). All of them bent in a semi fantasy setting, though. I mean, don't expect with real kabbalistic "art" to animate a golem or something, don't expect with real treatises on necromancy to "raise" skeletons, zombies and specters etc. It brings a nice feeling with the lore about kain, the incoming apocalypse, the gloom and doom and so on. Feels like a darker, crazier, loonier version of real world paranoia- sorry, i mean religion and sect teachings...

Tremere dungeons, alchemical research, corpses and "divining the future from ripped entrails" (as a tremere himself suggests in game, and as that once had been a real divinatory method), had a nice touch of macabre disgust, as well. You can't go wrong with this one. Highly recommended.

Heimdall and Heimdall 2) feature Norse mythology.

Because even GOG couldn't get it to run right. The DLC about the burned man is largely inspired by Mormonism.

The King Arthur Roleplaying Wargame has Christianity as one of the axis that you can move along. Being christian can grant you units like Crusaders and such. The other direction is the Old Faith which is a real religion as well - though I'm not sure how accurate it is.

Why has nobody mentioned the whole Mount & Blade series yet?
http://www.gog.com/game/mount_blade
http://www.gog.com/game/mount_blade_with_fire_sword
http://www.gog.com/game/mount_blade_warband
http://www.gog.com/game/mount_blade_warband_napoleonic_wars
http://www.gog.com/game/mount_blade_warband_viking_conquest

Although you play exactly the role of a medieval leader (and later his heir and the heir of this one, etc...) it may not be considered as a role-playing-game, but Knights of Honor is as historically detailed as it gets. You can choose three different eras of the middle ages which are alle very well represented.
Difficulty is set by your decisions. If you're choosing to make your nation christian, you'll have to fight against heretics and muslim states every time the pope says so, if you choose the muslim side you're at war with christian countries and if you choose to play a pagan scandinavian state while trying to stay away from the abrahamitic religions, you're screwed and have a hard time.

Crusader Kings II. Not an RPG per se, since normally is considered to be a grand strategy game, but I've had a pretty good RPG experience playing it. The only "problem" with it, is that the base game is pretty much Christianity-centric and you'll need the expansions if you want to play with a non-Christian family. That means it's gonna be somewhat pricey unless you buy it during a sale. Still waiting for a GOG release, but this has been already discussed previously.