Songs about Despair

[Hiro The Dragon King]

The Wall

[PotatoBaron]

http://www.youtube.com/watch?v=f8hT3oDDf6c&ob=av2e
Alice in Chains, Down in a Hole. Old but good.
http://www.youtube.com/watch?v=cs-XZ_dN4Hc
Pearl Jam, Black. A little less obvious, but the despair becomes evident later, though the lyrics are a little odd to hear due to pearl jam being near-impossible to understand sometimes. (in my opinion)
two of the sadder songs I immediately thought of.

[Kanti13]

Nine Inch Nails - Hurt
Silverchair - Nobody Came
Blue October - Weight of the World
Some that come to mind. Also some other songs by these bands. Early Stained too.

[Azexous]

You could try either:

Millstone by Brand New, specifically the alternative one. The original isn't as sad.
http://www.youtube.com/watch?v=tms5SyUotpY

or

On my Own by The Used
http://www.youtube.com/watch?v=Ho9L2J2RIy8

[Emotive]

There are tons of songs about despair from tons of different genres, what genre are you looking for?
Personally I'd recommend early Swans.
Nobody
Coward

Or um, later Swans.
Failure

[TritioAFB]

There are tons of songs about despair from tons of different genres, what genre are you looking for?

Not exactly one genre, it can be any genre: Rap, Rock...