I probably enjoy lyrics more than the actual songs most of the time. In your opinion, what band has the best lyrics?
I really enjoy Danial Davey’s lyrics (Cradle of Filth), also Elijah Alleman (Deadsy) ranks high on my list.
I don’t know about “best”, but I enjoy The Shins’ lyrics.
Billy Joel
Lyle Lovett
Keith Reid
Loudon Wainwright III
Jethro Tull strikes me as having some of the best lyrics ever.
Not a band, and I know lots of people find him pretentious, but I’m actually quite a sap for Sting’s lyrics. And while I’m not familiar with their whole body of work, I’ve always found the lyrics to this Blues Traveller song to be kind of clever.
I think Rush has mostly evocative and intelligent lyrics. You do have to deal with Geddy Lee singing them, though. That’s a total love/hate thing right there.
Modest Mouse has the best lyrics in rock music history for my money. I usually point to Sytrofoam Boots as their best, but check just about any song, really.
Peter Gabriel
Bob Dylan (kind of a duh)
Richard Thompson
ETA: None of these are bands - so sue me.
Chris Cornell (Soundgarden, Audioslave) writes some pretty good lyrics too.
I was just thinking of him. Yes, he does.
Gentle Giant had some interesting lyrics.
Grateful Dead
Van Morrison
Neil Young
Paul Simon
Talking Heads (David Byrne solo stuff as well
I didnt mention Dylan, as he is probably the measuring stick for comparing all others…
I’m not a huge lyrics man, more into sounds first, words second. But even I have to bow before the awesome wordsmith that is Morrissey and The Smiths.
When your lyrics are used by other people for a band name, or a film title, you know you’re making a splash. Panic at the disco, Hang the DJ, Girlfriend in a coma, Shakespears sister etc etc. Of course part of this is just because The Smiths were a mighty, influential band; and like all great bands get namechecked a lot regardless of their lyrics. But there’s no denying the exceptional quality of Morrissey’s writing - he’s one of the rare few whose lyrics have passed into the general lexicon of the age. A British Bob Dylan if you like.
A less well-known example (in the US) would be Pulp. Jarvis Cocker is a gifted lyricist - I know this because I don’t particularly like the band at all, but still have to admire his words. His last solo offering was painfully bad, as well. So he’s following in the steps of the greats like Dylan and Morrissey there as he matures into his solo career.
Stephen Merrit Of The Magnetic Fields writes some amazing lyrics.
I always thought early Roxy Music had interesting lyrics.
I really enjoy the wittiness of The Trash Can Sinatras and the Rave-Ups.
Natalie Merchant and Phil Ochs are great at making a social cause listenable.
Tim Minchin and Camille West have a way with a humorous song.
Uncle Bonsai (they’re sort of halfway between Jonathon Coulton and Tom Lehrer.)
A Perfect Circle/Tool
‘Is your halo slipping down, to choke you now?’ Sweet I just made an APC station on Pandora and it started with the track I wanted to hear most. 
Snog
‘We are happy little proles, and we’re on our way to work.’
Skinny Puppy
‘in nervous convulsion crouches infant ape trembling in mothers shit
cage eyes tear less filled with contempt clinic mask experiment with
life and death smell lingering noxious mixed scent anxiety omnipotent doctor
grinds the cage door revealing loves primal instinct taken away’
KMFDM
‘Like a fiendish tropic virus
Spitting bile at all you whores
Razor-sharp tongue-in-cheek
Poking in your open sores’
I forgot two major ones.
Bruce Springsteen and Tom Waits.
Might as well include Johnny Cash and Leonard Cohen at this point.
Tom Waits has quite a way with words, though I was bummed to learn he didn’t come up with one of my favorite lines – “champagne for my real friends and real pain for my sham friends” (he was quoting the painter Francis Bacon, IIRC).
Tod Ashley (aka, Tod A.) of Cop Shoot Cop and Firewater is another great lyricist. The raucousness of his music belies the sharp wit and sensitivity of his words.