Dark/Demon's Souls have very brooding atmospheres. Not what I would call depressing really, but definitely very dark. And there are some moments in Demon's Souls that tugged a bit, and those were very well done Imo.
Nier also, it's kind of just one those games that makes you wonder how they ever got funding for it. A gem for anyone looking for some alternative/tragedy/depression.
For PS2, check out Ico/SotC (they also have that HD collection), Ico is beautiful in a sad way, SotC is mostly just sad. Both of these are highly abstract though, so maybe not your thing.
I wish I had some original suggestions, but atm I can't think of any games that have moved me much. Off to go find me a copy of Terranigma I guess...
Its only like 70 years away. By then, ill just be hitting my stride. Like the PS3. - Skul_
Telltale's The Walking Dead game is pretty depressing at times. Only four of the five episodes have been released so far for download, but there is a disc version being released in December with all five episodes included if you prefer a physical copy.