Peart was one of the first drummers I heard that really floored me. A friend in my freshman year of high school lent me Moving Pictures, and I remember being dazzled by all of the tom fills. His sense of composition is immaculate, each note he plays feels like the precise one for that particular moment. I also enjoyed his guest drumming on a few tracks with Vertical Horizon for a much more restrained version of himself.
Portnoy was one of the next guys to blow me away. The complexity, the speed, the variety of different sounds from all varieties of toms and effects cymbals, it went a level beyond Peart. And it was fun to watch, I remember getting Liquid Drum Theater even though I didn't yet own a drumset, and being spellbound watching him. I've since heard many guys who are even faster and more complex, and sure, after awhile you can spot that he doesn't have the deepest well of tricks and reuses ideas a bit too often, but few could make it sound as cool and musical as he could. The intro to "Paradigm Shift" is one of those parts that isn't nearly as complicated as it sounds, but I'm sure was played at many a Guitar Center afternoon to fool onlookers into thinking they were drum gods.
Here's my list. I might do short writeups tomorrow on a few of the top ones who didn't make the group list.
25: Anup Sastry (Skyharbor, Intervals)
24: Peter Wildoer (Darkane, James LaBrie)
23: Omar Hakim (Aziza Mustafa Zadeh, Weather Report)
22: Paul Roraback (Grammatrain, Gideon's Press)
21: Matt Garstka (Animals As Leaders, Louis de Mieulle)
20: Carter Beauford (Vertical Horizon, Dave Matthews Band)
19: Phil Collins (Genesis, Brand X)
18: Anika Nilles (Nevell, Jeff Beck)
17: Dennis Chambers (Niacin, CAB)
16: Terry Bozzio (Explorer's Club, U.K.)
15: Marco Minnemann (Paul Gilbert, Steven Wilson)
14: Ted Kirkpatrick (Tourniquet, Trouble)
13: Morgan Rose (Sevendust, Call Me No One)
12: Dave Weckl (Aziza Mustafa Zadeh, Chick Corea)
11: Steve Smith (Vital Information, Tony MacAlpine)
10: Dirk Verbeuren (Soilwork, Sybreed)
9: Ed Warby (Ayreon, Star One)
8: Neil Peart (Rush, Vertical Horizon)
7: Mike Portnoy (Dream Theater, Liquid Tension Experiment)
6: Gavin Harrison (Porcupine Tree, The Pineapple Thief)
5: Sean Reinert (Aghora, Cynic)
4: Martin Lopez (Opeth, Soen)
3: Ivar de Graaf (Kingfisher Sky, Within Temptation)
2: Daniel Liljekvist (Katatonia, Grand Cadaver)
1: Danny Carey (Tool, Volto!)
Honorable Mentions: Anders Jivarp (Dark Tranquillity), Art Blakey, Bill Bruford (King Crimson), Billy Cobham (Mahavishnu Orchestra), Bobby Jarzombek (Spastic Ink), Brann Dailor (Mastodon), Buddy Rich, Chad Szeliga (Breaking Benjamin), Curt Cress (Passport), Daniel Moilanen (Katatonia), Dobber Beverly (Oceans of Slumber), Elvin Jones (John Coltrane), Gene Hoglan (Death), Hannes Grossman (Obscura), Jay Postones (TesseracT), Jerry Gaskill (King's X), Jerry McBroom (Bride), Jimmy Chamberlin (Smashing Pumpkins), John Macaluso (Ark), Martin Axenrot (Opeth), Matt Halpern (Periphery), Matt Thompson (Aghora), Max Roach, Morgan Agren (Kaipa), Richard Christy (Death), Simon Phillips (Derek Sherinian), Simon Zimbardo (Aziza Mustafa Zadeh), Steve Gadd (Al DiMeola), Stewart Copeland (The Police), Thomas Lang (Paul Gilbert), Tony Williams, Van Williams (Nevermore), Vinnie Colaiuta (Frank Zappa), Virgil Donati (Planet X), Yanic Bercier (Quo Vadis)