Here are mine, did a list of about 30-odd:
Bob Dylan
The Smiths
Van Morrison
The Cramps
Fairport Convention
Jimi Hendrix
Talk Talk
Joni Mitchell
Neil Young
Velvet Underground
Radiohead
Aretha Franklin
The Wedding Present
The Pogues
Tom Waits
Throwing Muses
PJ Harvey
Neutral Milk Hotel
Gillian Welch
Stiff Little Fingers
Pixies
Sonic Youth
Tori Amos
My Bloody Valentine
Prince
Joy Division
Kate Bush
The Clash
Frank Zappa
Patti Smith
Rolling Stones
Led Zeppelin
Who are yours?
The Jam
Nick Drake
The Pogues
Bob Dylan
Richard Thompson
Christy Moore
The Specials
The Smiths
Stiff Little Fingers
Elvis Costello
The Clash
To name but a few.
Robyn Hitchcock
Gorky's Zygotic Mynci
The Fall
BBC Radiophonics Workshop
Undertones
Status Quo
Specials
Aztec Camera
Broadcast
Delgados
Mogwai
Pixies
Madness
Tiger
Sonic Youth
Pavement/Malkmus
and, erm, loads more great bands.
Quote: Rob H @ July 17 2009, 9:25 AM BSTThe Jam
Nick Drake
The Specials
Elvis Costello
Good calls that I didn't mention.
Quote: john lucas 101 @ July 17 2009, 9:27 AM BSTThe Fall
Undertones
Delgados
Mogwai
Pavement/Malkmus
Love all these and HMHB too. 
I listed my main faves, but really I could've gone on all day listing ones.
Best live gigs I've been to: Dylan, The Cramps, Radiohead, PJ Harvey and The Wedding Present.
Without compiling a whimsical, non-exhaustive list, I'd like to nominate Paul Rodgers as a favourite artist.
I watched him on Sky Arts last night performing with Queen in 2005. Link this superb vocal performance to his days with Free and Bad Company and you have a brilliant front man with a career spanning 40-odd years.
The Smiths
Joy Division
David Bowie
Why do so many comedian/writers love the smiths?
Quote: Tom G @ July 17 2009, 9:39 AM BSTDavid Bowie
Yeah, Bowie is ace too of course. I like Hunky Dory, Station To Station and Scary Monsters best. Low is great too. Oh and Aladin Sane is better than Ziggy.
Quote: Jackson Neil @ July 17 2009, 9:39 AM BSTGood calls that I didn't mention.
Love all these and HMHB too.
Bugger forgot those. Additions:
Half Man Half Biscuit
David Bowie (particularly Low)
Quickspace
Best ever gig: Quickspace, The Garage, 1995 (I think).
Daniel Merriweather
Vixen
Kula Shaker
Level 42
Robert Palmer
Boys 2 Men
Falco
London Boys
Wang Chung
The Verve
Five Star
Mel and Kim
Shakin Stevens (but only with the Sunsets)
Quote: chipolata @ July 17 2009, 10:03 AM BSTDaniel Merriweather
Vixen
Kula Shaker
Level 42
Robert Palmer
Boys 2 Men
Falco
London Boys
Wang Chung
The Verve
Five Star
Mel and Kim
Shakin Stevens (but only with the Sunsets)
Ah, Vixen. Sleevenotes that you could wank to. 
Quote: Rob H @ July 17 2009, 10:16 AM BSTAh, Vixen. Sleevenotes that you could wank to.
Mel and Kim were pretty wankable offable too...until one of them died of some terminal illness. 
Here's a few of my favourite bands/artists off the top of my head:
The Who
The Band
The Smiths/Morrissey
The Divine Comedy
The White Stripes
Ryan Adams (Not Bryan!!!)
The Kings Of Leon
Bob Dylan
The Doors
The Rolling Stones
Elastica (first album I bought, still ace)
Quote: chipolata @ July 17 2009, 10:20 AM BSTMel and Kim were pretty wankable offable too...until one of them died of some terminal illness.
Man's gotta know his limitations.
The first album I bought was Rick Astley.
The first single was Stand and Deliver by Adam and the Ants which is marginally better.
Quote: Rob H @ July 17 2009, 10:24 AM BSTThe first single was Stand and Deliver by Adam and the Ants which is marginally better.
That's a great song. Pity Adam succumbed to madness, fatness and baldness.