I have to agree with Bloodlines and Witcher titles, mentioned more than 3 times already. I would also like to add Symphony of the night, too. Whole story with protagonist becoming the antagonist and the secret inverted castle asspull was something else entirely. Haven't seen more plot twists in any game ever after.

Here's some serious games :D

The Solus Project
Inquisitor
The Journeyman project games
The Cat Lady
The last express

The Sniper Elite series (1,2, & 3) fits your requirements. Each game has a standalone serious storyline.
The spinoff series: Sniper Elite: Nazi Zombie Army is more fantastical, but still follow a serious storyline.
Your enjoyment of the Sniper Elite series will vary depending on much you tolerate Vin Diesel voiceovers,
and whether the simple joys of the bullet cam sicken you(bullet cam can be turned off) or amuse you.

I dunno, I think the Witcher games have their share of comic relief. For the most part they're serious, but then you have stuff like a private detective named Raymond Maarloeve, Odrin's antics, just about everything involving Dandelion, that side quest in Witcher 2 about the guy collecting harpy feathers, etc.

Anything with good story, always contains a carefully measured dose of comic relief!

Just wanted to mention something a lot of you guys/gals seem to be misunderstanding.
SERIOUS =/= REALISTIC
Games which I listed, I see as more or less serious, but of course they are not realistic at all.
Realistic is a different beast.
And since games are exits, they often take us far away from real(istic).

A serious game by my definition is being serious about it's fantasy world and story.
Not adding things that undermine it.
The world itself must also be serious by design. If it is designed as one big joke, then of course it doesn't matter whether the game jokes about it further.
This about sums it up.

I know, sometimes the line between non-serious and merely-very-unrealistic is very thin.
It may also be, as someone suggested, quite a bit subjective.

Rare is a 100% serious game. But it varies a lot how easy it is to avoid the easter eggs and silly jokes.

I know I'm not too active in this discussion, but as always I like more to simply hear opinions (than to argue).
Thanks for the comments so far.

Videogames aren't serious, c'mon chums.

Of course Torment is the tops, but there are others.

I second Inquisitor - excellent story, writing, atmosphere, all serious, mature, dark, and deep and interesting.

Another that might fit what you're looking for is Pathologic.

Knock Knock's pretty awesome, too!