This is way too hard. My real answer is a list of ten Smashing Pumpkins songs, but I'll limit myself to one per band.
"Wound" - The Smashing Pumpkins
"A Murder of One" - Counting Crows
"Life Like Weeds" - Modest Mouse
"Sleep" - Godspeed You! Black Emperor
"A Distorted Reality Is Now a Necessity to Be Free" - Elliott Smith
"Paranoid Android" - Radiohead
"Temporarily Blind" - Built to Spill
"P.S. You Rock My World" - The Eels
"Dendron" - The Hotelier
"Into the Streets" - Twilight Singers
I could probably make this list again in a couple hours and have half of it replaced. It feels at the very least that "Blister" by Jimmy Eat World, "Raspberry Cane" by Youth Lagoon, "Limousine" by Brand New, "I'm The Ocean" by Neil Young and Pearl Jam, "Fight Test" by Flaming Lips, "Acrobat" by U2, and something by The Antlers / The National / Sigur Ros should be on there.