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I can't limit myself to just 3, but just off the top of my head:

Steve Gadd
Duke Ellington
Buddy Rich

And you want to know why...

Steve Gadd does things that no one has ever thought of before.
Check this out. That's him showing his grove on Paul Simons "50 ways to leave your lover." A song that just baffled me for the longest time till I saw that video. Left hand on the hi-hat...slaps forehead. It's genius.

Buddy does things no one else can do Watch This! Excuse my french, but are you ******** kidding me? That is the s**t.

And Duke brought it all to the world. He brought New Orleans and Chicago and Kansas city and Harlem Jazz to places like London and Berlin. He composed some of the most gorgeous arrangements ever, and made it accessable(sp). He was the Duke. he introduced people like Jimmy hamilton, Johnny Hodges, Cootie Williams, Cat Anderson, Buster Cooper. Songs like Caravan and Harlem...Good stuff.

Lol, we don't bother limiting yourself, just as long as you can say why, which everyone seems to be fine at wink

I don't think I can limit myself either razz but here's some of my faves..Really quickly, too, because I've got homework to do.

Art Tatum: As a piano player, you can't help but idolize the guy that played a song at 400 bpms. He's just incredibly talented, bit of a pianist god. His tunes go from high energy to slow and calm, and, well, he's just amazing.

Billie Holiday: Because I admire her for her. I'm actually not a big fan of a lot of her stuff, but she did some amazing things with what was given to her. Strange Fruit got me hooked- a political message, in an amazing song, which took a lot of bravery at the time. She went through a lot of stuff and still turned out some great tunes.

Duke: Pretty much what Frustrated said. He brought jazz to the world (thank you..) But he also came up with tunes that are super catchy, interesting musically, and accesible (sp) to anyone, in most respects.

one more. Benny Goodman, because he did things with a clarinet that I didn't think were possible, particularily with that instrument. And personally, as a clarinetist, it starts and ends with him.

Sure, there's tons more, but it's late and I'm tired......

Hubert Laws, because he plays flute fantastically in any genre!
Bobbi Humphrey- She makes me want to get out there and get my feet wet.
Kenny G- I just love every song he's ever made. ( I'm not feeling very loquacious today, sorry. sweatdrop )

Greats as in performers or big band groups or what? lol!

Count Basie-definately! Need I explain? ^^

I'm partial to my sax guys-Coltrane and Parker...and Cannonball.

Stan Kenton or Chick Corea or Art Blakey-some of their stuff-Maynard Ferguson [my past sax instructor opened for him in KC not that long ago]...

Been doing Jazz Catologing Project-so I've had total access to all the jazz records and what not here in our music library-it's fabulous!
Guess that might be why but-I really can't pic one group or performer or even just 3 greats-there's so many names out there and just so many amazing jazz musicians...sorry!... sweatdrop