Damn, I fotgot about Evelyn Glennie. She does play a marimba, after all.
I’d say non-trap-wise the Hip Pickles are my favorite rudimental drummers.
Steve Gadd, and from mainstream: Neal Peart, Stewart Copeland, and Keith Moon.
Danny Carrey, Kieth Moon, and Chad Smith from the Red Hot Chili Peppers.
Animal from the Muppet Show
Levon Helm.
I’ll add a vote for Neil Peart, who I think is brilliant.
But this is a little over the top:
I think only Peart qualifies as being at the 'pinnacle of his instrument. Geddy and Lifeson are both excellent musicians and very good with their instruments, but I don’t think anyone would consider them to be the best bass and lead guitar players. I’d put 'em both in the top 100, though.
Back to drumming… How about Ringo Starr? Much underrated both as a drummer and an innovator. Listen to the Beatles sometime and try to tune out everything but the drums, and listen to what Ringo was doing. Great stuff, very innovative for the time. When the Beatles got their first recording contract, they asked Ringo to join the band because he was one of the most highly acclaimed musicians in Liverpool at the time. They considered getting Ringo to be a pretty good coup.
First off, Dennis Chambers is not a jazz drummer!
Billy Cobham
Lenny White - From funk to fusion to straight ahead jazz.
Marvin “Smitty” Smith
Ben Riley - I saw this guy play recently with a pair of leather gloves on and they didn’t even fit tight. Go figure.
No, I’d put Geddy Lee at the very pinnacle of Rock bassists, no doubt. But Alex Lifeson himself has said he’s not the best because he gets lazy. Between tours and recording sessions he stops playing and has to relearn things.
Oh, and it’s Neil Peart…all the way.
Behind his is Stewart Copeland. SC has the best damn high-hat technique I’ve ever heard. It’s just astonishing what he was do with two brushes and a high-hat. He doesn’t even need the other gear.
Aah…Levon Helsm is great too…not easy to sing and drum.
Copeland also…even his new stuff with Oysterhead (Les Claypool, Trey Anastasio) is pretty incredible.
See, I don’t get this. I realize that the Red Hot Chili Peppers are getting set to be the Who of our generation, and a special edition “Chad Smith Signature snare drum” has been successfully marketed, but what is really so special about Chad Smith’s drumming? What Chili Peppers song should I be listening to to be reminded?
D’oh! I forgot Steve God-- I mean Gadd.
As to Chad Smith as far as his sig snare drum, that’s a pile. It’s a regular G.I. snare that sounds nothing like the Ludwig Black Beauty and other gourmet snares he uses in the studio. Not that it’s a bad drum, just an act.
He’s just really modest 
Ditto on Matt Cameron. He’s my ultimate dream drummer: tight, creative, happy with neat little rythmns that take simple songs up a notch. I wish I had been more impressed with Riot Act’s songs, but Matt’s drumming definately wasn’t the problem (and he was great on their previous album too).
Cubby.
Dammit, what about Meg White? Looks so tiny there behind the kit but she hits them drums hard.
Also, I’ll second Dave Grohl, Jimmy Chamberlain and Chad Smith.
I’m going to throw Larry Mullen out there. With U2, so much emphasis is placed on Bono’s voice and Edge’s guitar playing that the truly amazing rhythm section just gets overlooked. Check out any U2 song and notice just how good the bass and drums parts are, particularly on With Or Without You, which effectively anchors the song so Bono and Edge can go wild.
Hmm… and the drummer from the Clash, just because of the great break that opens London Calling.
I saw him play with John McLaughlin and Joey Defranceso at the Bottom Line a few years back. It sounded like Jazz to me!
Danny Carrey (Tool), Neil Peart (Rush), Stewart Copeland (Police) – I full-heartedly agree with all of those nominations.
Does anyone love Sheila E.? I’m thinking of her one big pop hit, The Glamourous Life. She did all the percussion on that album, and did most of it on several Prince albums. Now, IIRC, she does lots of jazz, as she was brought up as a jazz percussionist, by her father, who is some famous jazz guy. I know nothing of jazz, but I think Sheila E. is one of the most talented, underrated percussionists anywhere. Just wanted to make sure y’all don’t forget about the two or three really great chick drummers.
I’d also nominate Lenny Kravitz’s drummer, the chick with the huge 'fro.
First off, whether I’m a drummer or not, I’m going to have to fight a bit of ignorance with this comment
That’s a bit broad, don’t you think? Your reasoning would put Iron Butterfly at the top of the pyramid and ignore the history of percussion that has come before and after it. Sorry, but that’s ignorant. At least be indifferent for a better reason.
Now that that’s out of the way, a few names:
Buddy Rich An amazing egotist with undeniable talent, I’ve never heard his snare work equaled.
Terry Bozzio Played with Zappa on the infamous “Black Page”, a very clinical player and a very, very nice guy.
John Stainer formerly of Helmet, now with the underappreciated Tomahawk. He used to nail his whole set to the floor.
Doug Scharin Played with June of 44, now on a solo project entitled HiM, an amazing blend of rock and jazz.
Ryan Rapsys Of Euphone, also 5ive Style and Heroic Doses. Absolutely blistering, completely underrated player, highly influenced by Elvin Jones, who deserves a catagory all his own.
Elvin Jones whose ride work was aptly compared to “riding on a westbound train that’s traveling on top of an eastbound train”, his subtlety and phrasing are amazing, and impossible to transcribe.
Stuart Copeland As many have mentioned above. I mean, Peter Gabriel had him play on “Red Rain” using ONLY his hi hat!
Daniel Howard of Cinematic Orchestra, another vastly underrated player and band.
Vinne Colaiuta Next to Steve Gadd, probably one of greatest session players ever, who also worked with Zappa in his early years.
Joey Baron His work with John Zorn has always left me speechless, the man can play anything. When I saw him he would de-tune his snare with his left foot while playing. Probably my favorite all-around player.
I met Sheila E. once at the Drum basement in Veneman’s music in Rockville, MD (I met Steve Gadd at the same place once). She was in to give a talk and play a bit. She can bang 'em pretty effectively.
And she autographed an 8x10 “To the MEN(!) of the Drum basement…Love, Sheila E.”
I think I found God that day.