Neil Peart
Rod Morgenstein
Mike Portnoy
Simon Phillips
Dave Weckl
Lenny White
Billy Cobham
Terry Bozio
Phil Collins (Early Genesis when he was a drummer & not a singer!)

I'd like to play with Tom Ardolino, Charlie Watts, Frank Beard. Groove guys who swing.

Wishbass, that drummer would Ian Mosley, yes he's still with them (and playing spectacularly to this day) and he's also on my wishlist, along with the usual suspects Neil Peart, Bill Bruford, Alan white (Hey, he had to learn Bill Bruford's stuff in 2 weeks!)Phil Collins, Nick D'virgillio, Gavin Harrison

In addition to many mentioned, how about Jimmy Carl Black? his tribal sounding drums in the Mothers of Invention was cool...also Dale Crover of the Melvins

Thanks Ken!That album was so magical.I really need to check out the post-FishMarillion.I've heard some stuff here and there and like what I've heard.I recently Discovered a band called Riverside(they are a must) that really got started from their love of Marillion,and that has inspired me to start making some Marillion purchases,as well as Fish's solo work.

NOT the drummers from Spinal Tap, thank you.

Trilok Gurtu blurs the distinction between drum set players and conventional percussionists:
http://www.youtube.com/watch?v=0kxnfCSkWzs&feature=related
 
Paco Sery:
ttp://www.youtube.com/watch?v=pNCRaXxv69w&feature=related
 
Manu Katche:
http://www.youtube.com/watch?v=--3QCzDFTtE&feature=related
 
Omar Hakim:
http://www.youtube.com/watch?v=qj8bGVWo6LY&feature=related
 
Narada Michael Walden, Vinnie Colaiuta, Jeff Sipe, Simon Phillips, Steve Gadd....and the guys I currently play with: Paul Costa, Peter Curzon and Sam Markewich!

Can't believe I didn't mention Manu Katche!I need to check the others out as well.

I played in a band in the early 1980's that the Bellamy Brothers drummer sat in with. Usually, we all left the stage for the drummers solo, but when he started, I could clearly hear the melody of the song in his solo. I stopped dead i  my tracks to listen to this amazing display of musicianship! Nothing flashy, just music.

I love many that have been already mentioned here but we can't forget ; Jerry Granelli , Joe Morello, Mike Clark ,Gene Krupa ....I know, I will think of more ... ... ...

Clive Bunker is hugely underrated. His playing on Stand Up was a real eye opener for me - up there with Ginger Baker and Mitch Mitchell.

David Garibaldi & Steve Gadd are two that I'd dream to play
A set with.

Who played drums on the first King Crimson record?

Wasn't it Michael Giles?I think that's right

From Wiki,Giles orchestrated much of the compositional structure of the first Crimson album In the Court of the Crimson King,[1] and his ability to weave challenging yet seamless tempo changes and subtle melodic deviations into a piece is not only evident in the compositions, but also in his highly elaborate and skilled drumming. He was most notably the first rock drummer to use more than one bass drum, so that he could play faster beats using those drums.