I have SO many favorite bands I'd prefer to list them by decade. Here goes...
late '60s/early '70s:
The Velvet Underground, Bob Dylan, The Beatles, Joni Mitchell, Nick Drake, John Lennon, Neil Young
mid-to-late '70s:
Bruce Springsteen, Tom Petty, The Police, Talking Heads, The Pretenders, The Clash, Elvis Costello, Joe Jackson, Rickie Lee Jones
'80s:
U2, Peter Gabriel, R.E.M., 10000 Maniacs, Paul Simon (later) (couldn't think of anything else...)
'90s:
Counting Crows, Barenaked Ladies, Pearl Jam, Toad the Wet Sprocket, Gin Blossoms, Oasis, Radiohead, Dave Matthews Band, Alanis Morissette, Tori Amos, Better than Ezra, Goo Goo Dolls
'00s:
Coldplay (early), The Killers, Beck (later), Wilco, Feist, Guster, Death Cab for Cutie, Regina Spektor, Joanna Newsom, Snow Patrol, The Shins, The White Stripes