I'm still a very new jazz fan and have mostly just listened to Jamie Cullums records, which I really like.

Any jazz fans here who can recommend good jazz artists?

Jamie Cullum? Well, at least you want to improve. ;)

I'm not really knowledgeable about Jazz, but I can tell you a few well known artists: Stan Getz, Herbie Hancock, Dizzie Gillespie, Count Basie, Duke Ellington, Ella Fitzgerald, John Coltrane, Miles Davis, Sarah Vaugn, Nina Simone, Billie Holiday.

Like Rock, Jazz has a lot of subgenres. But there are a few jazz essentials I would recommend from the 50s and early 60s (Cool Jazz):

Charlie Parker - Now's the Time
Miles Davis - Kind of Blue, 'Round About Midnight, Birth of the Cool
John Coltrane - Blue Train, Soultrane, A love Supreme
Dave Brubeck - Time Out
Cannonball Adderley - Somethin' Else, Know What I Mean?
Bill Evans - Trio 64, Everybody Digs Bill Evans, Portrait in Jazz
Sonny Rollins - On Impluse!
The Art Blakey Quartet - A Jazz Message
Oscar Peterson - Night Train
Stan Getz/Charlie Byrd - Jazz Samba

Chandos' recommendations are good, but might be a bit difficult to get into if you're new to jazz. You might want to start out with some older jazz recordings by artists that are a bit more traditional: Fats Waller, Billie Holiday, Django Rheinhardt and Louis Armstrong come to mind.

Django Reinhardt, Charlie Parker and Dizzy Gillespie.

Thelonious Monk. Josh Redman is pretty great too, if you're looking for something newer. I've never been able to get into Coltrane, myself. I find him overrated - but that's me.

Some great classic stuff recommended here -- I would certainly go with 'Bird', Coltrane, and Davis. But I really love Louis Armstrong, Dizzy Gillespie, and Buddy Rich (although he may be more Big Band).

For vocals try the Manhattan Transfer. Their greatest hits would be a good start (just ignore the popish 'Boy from New York City'). Their rendition of Birdland is fantastic.

There are a lot of subgenres in the jazz-scene. (Yeah, HB would not agree with that :p )
There's Cool, Bee-Bop, smooth, dixie, fusion, big band, free, and others. Any idea what kind of jazz you like.

My favs: Herbie Hancock, Stan Getz, Dizzie Gillespie, Art Blakey & The Jazz Messengers, John Coltrane, Adderley, Sonny Rollins and Nina Simone.
(Fabius and Chandos mentioned those too.)
Not too free (not too much wild improvizing) and not too 'restricted/bounded' as the bigbands.
Miles Davis has much improvizing. Some people might find that annoying, not able to find any logic in the music. So if you want a somewhat more organized style of jazz you take Big Bands like Glenn Miller's or those of Benny Goodman or Tommy Dorsey, but if it comes to BigBands, I prefer Count Bassie or Duke Ellington.

One of my favourites is Herbie Hancock's Cantaloup Island. His later stuff is more keyboards and electric stuff and less 'jazzy', imo.

For very accessible jazz - Miles Davis - Kind of Blue.

Pat Metheny is a good contemporary introduction as well, although after a few albums, it all starts to sound the same.

Jamie Cullum is cool.

My only jazz related album is "Saxuality" by Candy Dulfer.

Nils Petter Molvaer. Great musician.