This is my list that I keep updated as my interests change.
Grateful Dead, Sublime, Jimi Hendrix, Umphrey's McGee, moe., Keller Williams, Allman Brothers, Cake, Dave Matthews Band, Dire Straits, Mark Knopfler, Kansas, Phish, U2, Widespread Panic, Béla Fleck & The Flecktones, Beastie Boys, A Tribe Called Quest, STS9
I own at least one album of all of the above bands except for Hendrix, but I plan on getting one soon.