There aren't any songs that make me sad, I don't think. I can't bring one to mind anyway. There are songs that sometimes make me think of the sad stories behind them (Kirsty MacColl, The Carpenters) but there aren't really any that evoke sad times for me.
There are a few that I like to wallow in though, indulge a sort of studied sadness, a bit like the slim volume of poetry you might take to moon around in a cafe for a bit. It's not real sadness, it's cinematic gloom, ersatz nostalgia.
The best of these is the Kings Singer's version of The Slow Train. A lovely evocation of a less efficient time, and the male choir highlights the splendid anachronism of it all. It makes me sad like Passport To Pimlico does - oh why can't we go back to a past that never existed?
If you're in a spotify compliant geography you can listen here. If you're not, this might work. And this Lemon Jelly track samples it to good effect.