My grandma gets mad at me when I call classical music songs. She says, "There's no singing, so its not a song!" She was a classical singer, not to mention she's my grammy, so she wins.
John Lennon - Imagine (already said, but can't be said enough)
Beatles - Across the Universe
Johnny Cash - Hurt (saddest song ever)
Neil Young - The Needle and the Damage Done
Also some I think are the greatest, but probably aren't to anyone else:
Radiohead - Creep
Nirvana - I Hate Myself and Want to Die, and Pennyroyal Tea
Everclear - Strawberry (not the new sissy fufu stuff)
Foo Fighters - Everlong
Nine Inch Nails - i do not want this, and pretty much any other song he sings
Gary Jules - Mad World (Donnie Darko and Gears of War commercial)
There are certain songs that are just so good, you have to stop listening to the music for a while for it to sink in. The songs I listed do that for me.