Portal is a good answer. It has a dark sense of humour, a lot of cinematic style, and the music is a very effective atmosphere builder. The one problem is the world, which is entirely a laboratory complex and most of the game is spent in testing rooms. If you bring in the larger Half Life universe, which that laboratory complex is allegedly located in, it actually makes it worse, as the serious dystopian setting of Half Life clashes with the wacky antics going on in the Portal world. Both incredible games, though. Half Life does have a cast of strange creatures and epic locations, as well as some amusing writing, so between the two worlds a pretty good analogue to Oddworld can be seen.
An early story sequence in Portal which I think is cool:
http://www.youtube.com/watch?v=aXYuL4yo0tM
And this scene in Half Life 2: Episode 2 shows off some aliens:
http://www.youtube.com/watch?v=mT-tV7zOEPU
Damnit, watching those makes me want to play a new Half Life game.
Bioshock is a good answer, too. Great, original world, dripping with atmosphere. I'm actually playing through the first one, which I've yet to finish, at the moment. There are definitely things about it that remind me of Oddworld eg. the plasmid adverts that cheerfully explain the destructive power of the ability remind me of the sense of humour in some of the Oddworld information points.