"Song to the Siren" by This Mortal Coil, a sort of supergroup made up of artists on the 4AD label. The singer is Liz Fraser of the Cocteau Twins, who also sang later with Massive Attack. She has a beautiful voice.
"The Passenger" by Iggy Pop. I don't understand why this isn't (even) more popular than it is. The feeling of life as triumph is wonderful.
"Sweet Jane" by the Velvet Underground. Probably the best song ever (and, yes, I know that's a stupid, or at least naive, claim--I'm embracing the naivete). A celebration of love and faith in all things good that perhaps only a bunch of despairing junkies could get away with.
"Southern Mark Smith" by the Jazz Butcher. The Jazz Butcher did a great cover version of "Sweet Jane," but this is his best song. "Girlfriend" and "Big Saturday" are worth tracking down too. The Mark Smith in question is the singer from The Fall, known for his cantankerousness, nonconformity, and way with words.
"Head Full of Steam" by the Go-Betweens. Not much of a video, I'm afraid, but a song good enough to make up for that (the official video is unwatchable). Guest vocals by Tracy Thorn. "Just to chase her, a fool's dream..."
"Two Star" by Everything But the Girl. (Two star is the lowest, cheapest grade of petrol/gasoline.) Just about any song sung by Tracy Thorn would do, but this one is lovably despairing, rhyming "disarray" with "hey!" It's the most "I'm not OK/You're not OK" song I know, by the woman who once managed to write a terribly sad song about being too happy.
"It Can be Done" by the Redskins. Turns out it can't, but it's still a moving ideal, and the catchiest Marxist propaganda you'll ever hear. "Look to Petrograd/Look to Petrograd, look to Barcelona/Fight against the land-/Fight against the land- and the factory-owners."
"Pressure Drop" by Toots and the Maytals. Feels a bit token here, but I love it. Best played very loud.
"Fade Into You" by Mazzy Star. If you've got this far through the list then you probably know this already, but it's hard to leave it off the list. Not a band I know at all apart from this song though.
"Rusholme Ruffians" by the Smiths. Hard to pick just one song by this band, and it could have easily been "Miserable Lie," "Pretty Girls Make Graves," "Jeane," "Cemetery Gates," "Handsome Devil," etc., etc. "Handsome Devil" is great for its observation of the world as experienced ("All the streets are crammed with things/ Eager to be held..."), "Miserable Lie" has great unconnected couplets ("What do we get for our trouble and pain?/ Just a rented room in Whalley Range" and "I know that windswept, mystical air/ It means I'd like to see your underwear"), and "Pretty Girls Make Graves" has good jokes (the woman's voice asking "Oh really?" after the title is sung, the reversal of familiar gender roles ("she's too rough and I'm too delicate"), and my favorite joke about free will ("I could have been wild and I could have been free/ But nature played this trick on me")), but "Rusholme Ruffians" wins because Rusholme is very close to where I went to high school and I like the line "I might walk home alone/ But my faith in love is still devout." Not very funny, but far from despairing.
That's ten, so I'll stop there. But I might also have included "New Dawn Fades" by Joy Division, "Marble Lions" by Saint Etienne, "Love Song" by the Damned, "Big Sky" by the Kinks, and many more by others. I'm tempted to do a top ten albums and favorite bands as well, but I'll try to resist being quite so self-indulgent. At least for a while.