I just wrapped up Malamud's The Assistant the other day, and it was definitely a depressing book in the sense that most of the characters cannot escape their "fate" and better their situation. Even when things seem to be turning the corner, fate intercedes again and drags them back down. I actually thought the book probably should have been called Crime and Suffering. There is a shout-out to Crime and Punishment in novel, but I would say that even though one of the characters does seem to be striving for enlightenment at the end, this still doesn't seem to offer up any significant spiritual release/relief as one might find in Dostoevsky or for that matter Solzenheitzen or Wiesel, but just a broader back, so to speak, for more suffering. The punchline of course is that the assistant is in training to become a Jew.
Someone on Goodreads said it was the bleakest book they had ever read. I would say it is close but not the bleakest book of all time. Incidentally, Dickens's Bleak House does have good things come to some of the characters, so it isn't in the running at all.
In my view, a bleak book focuses on characters that cannot escape their fate, and in particular has characters that attempt to improve their lot but cannot for one reason or another (often being deliberately pulled down by others jealous of their attempt). As alluded to above, bleak books don't really offer much in the way of spiritual consolation (even if it is only the consolation of the weak that Nietzsche scorned). They have a dark or jaded view of human motivations. They also don't have much to offer in the way of humor (which rules out one or two Faulkner novels that I might have nominated otherwise, as well as Adiga's The White Tiger). As Americans generally do prefer uplifting stories (even Cormac McCarthy tried to offer a light at the end of The Road), I find European authors are more likely to sort of indulge themselves in writing about the dark side of human nature.
I may come back and revise* this list (and I am certainly open to suggestions in the comments below), but here are my top 5 bleakest books.
1) A Fine Balance by Rohinton Mistry (I thought about making Such a Long Journey my number two, but decided that would just be piling on.)
2) This Way for the Gas, Ladies and Gentlemen by Tadeusz Borowski (An account of life in the concentration camps written essentially from the perspective of the capos. It focuses on how prisoners turned on each other. There is no redemption to be found here, and it isn't terribly surprising that Borowski committed suicide a relatively short time after WWII ended.)
3) A Tomb for Boris Davidovich by Danilo Kis (A look at the reach of international Communism)
4) Moravagine by Blaise Cendrars (Maybe the most misogynistic book I've ever read, the title character gets his kicks from murdering dozens of women. There is a very strained humor throughout the book, but it didn't do anything for me.)
5) The Assistant by Bernard Malamud
There are some books I have not gotten around to reading yet, but will most likely be in the running. This includes Celine (Death on the Installment Plan and Journey to the End of the Night) and Victor Serge (really all of his work, but Unforgiving Years is apparently the bleakest). Happy reading...
* I did wonder about adding Sinclair Ross to the list. His short story "The Lamp at Noon" is pretty bleak and is definitely in the running for bleakest short story. It's harder to decide about As for Me and My House. I think the fact that it ostensibly has a happy ending disqualifies it, but had he written the sequel where the couple is still inevitably dissatisfied with their lot (finally realizing that they were the authors of their own unhappiness), then that might crack the top 5.