I found about 12 lists of the best drummers of all time on the Internet and compiled them into one meta-list. The results are below: every drummer on three or more of the original source lists, organized by rank (that is, with the drummers on the most lists at the top). Drummers on the same number of lists are organized chronologically by date of birth.
Please note that these are not my personal opinions.
To see a version of this meta-list organized chronologically by date of birth, go here.
On 12 lists

Buddy Rich (US, 1917-1987)
Styles: Jazz
Associated with: Tommy Dorsey, Harry James
On 11 lists

John Bonham (UK, 1948-1980)
Styles: Rock
Associated with: Led Zeppelin
On 10 lists

Dave Grohl (US, 1969- )
Style: Rock
Associated with: Nirvana, Foo Fighters, Them Crooked Vultures
On 9 lists

Keith Moon (UK, 1946-1978)
Style: Rock
Associated with: The Who

Neil Peart (Canada/US, 1952- )
Style: Rock
Associated with: Rush
On 8 lists

Gene Krupa (US, 1909-1973)
Style: Jazz
Associated with: Benny Goodman

Stewart Copeland (US, 1952- )
Style: Rock
Associated with: The Police

Danny Carey (US, 1961- )
Style: Rock
Associated with: Tool
(Photo by Toby Canham/Getty Images)
On 7 lists

Max Roach (US, 1924-2007)
Style: Jazz
Associated with: Charlie Parker, Clifford Brown
(Photo by William P. Gottlieb)

Elvin Jones (US, 1927-2004)
Style: Jazz
Associated with: John Coltrane, the Elvin Jones Jazz Machine

Ginger Baker (UK, 1939- )
Style: Rock, blues, jazz, Afrobeat
Associated with: Cream, Blind Faith, Fela Kuti
(Photo by David Redfern/Getty Images)

Ringo Starr (Richard Starkey) (UK, 1940- )
Styles: Rock, pop, country
Associated with: The Beatles

Clyde Stubblefield (US, 1943-2017)
Styles: Funk, R&B, soul
Associated with: James Brown, Funkmasters

Billy Cobham (Panama/US, 1944- )
Styles: Jazz, jazz fusion, rock
Associated with: Miles Davis, Mahavishnu Orchestra

Dave Lombardo (Cuba/US, 1965- )
Style: Rock
Associated with: Slayer
On 6 lists

Charlie Watts (UK, 1941- )
Styles: Rock, jazz, blues
Associated with: The Rolling Stones

Tony Williams (US, 1945-1997)
Styles: Jazz, jazz fusion
Associated with: Miles Davis, The Tony Williams Lifetime

Steve Gadd (US, 1945- )
Styles: Rock, pop, R&B, blues, jazz, jazz fusion

Mitch Mitchell (John Graham Mitchell) (UK, 1946-2008)
Style: Rock, jazz fusion
Associated with: the Jimi Hendrix Experience
(Photo by Jim Marshall)

Terry Bozzio (US, 1950- )
Styles: Rock, jazz fusion
Associated with: Frank Zappa, Missing Persons

Phil Collins (UK, 1951- )
Styles: Rock, pop
Associated with: Genesis

Chad Smith (US, 1961- )
Styles: Rock, jazz-funk
Associated with: Red Hot Chili Peppers, Chicken Foot, Chad Smith’s Bombastic Meatbats
On 5 lists

Art Blakey (US, 1919-1990)
Style: Jazz
Associated with: Art Blakey and the Jazz Messengers

Carl Palmer (UK, 1950- )
Style: Rock
Associated with Emerson, Lake & Palmer, Asia

Alex Van Halen (Netherlands/US, 1953- )
Style: Rock
Associated with: Van Halen

Vinnie Colaiuta (US, 1956- )
Styles: Rock, pop, funk, jazz, country
Associated with: Frank Zappa, Joni Mitchell, Sting, Tom Scott

Dave Weckl (US, 1960- )
Style: Jazz, jazz fusion
Associated with: Chick Corea Elektric Band

Lars Ulrich (Denmark/US, 1963- )
Style: Rock
Associated with Metallica

Mike Portnoy (US, 1967- )
Style: Rock
Associated with: Dream Theater

Tomas Haake (Sweden, 1971- )
Style: Rock
Associated with: Meshuggah

Josh Freese (US, 1972- )
Style: Rock
Associated with: The Vandals, Devo, Guns N’ Roses, A Perfect Circle, Nine Inch Nais, Weezer, Sublime with Rome

Travis Barker (US, 1975- )
Style: Rock
Associated with: Blink-182
On 4 lists

Tony Allen (Nigeria, 1940- )
Style: Afrobeat
Associated with: Fela Kuti

Ian Paice (UK, 1948- )
Style: Rock
Associated with: Deep Purple

Bill Ward (UK, 1948- )
Style: Rock
Associated with: Black Sabbath

Jeff Porcaro (US, 1954-1992)
Style: Rock, jazz fusion
Associated with: Toto

Steve Smith (US, 1954- )
Style: Rock, jazz, jazz fusion
Associated with: Journey

Tommy Lee (Greece/US, 1962- )
Style: Rock
Associated with: Mötley Crüe, Methods of Mayhem

Matt Cameron (US, 1962- )
Style: Rock
Associated with: Soundgarden, Pearl Jam

?uestlove (Ahmir “Questlove” Thompson) (US, 1971- )
Style: Hip hop, neo-soul
Associated with: The Roots

The Rev (James Owen Sullivan) (US, 1981-2009)
Style: Rock
Associated with: Avenged Sevenfold
On 3 lists

Bernard Purdie (US, 1939- )
Styles: Rock, R&B, soul, funk, jazz
Associated with: James Brown, Aretha Franklin

Moe Tucker (Maureen Tucker) (US, 1944- )
Style: Rock
Associated with: The Velvet Underground

Carmine Appice (US, 1946- )
Style: Rock
Associated with: Vanilla Fudge, Cactus, Beck, Bogert & Appice, KGB, DBA, SLAMM

Bill Bruford (UK, 1949- )
Styles: Rock, jazz, jazz fusion
Associated with: Yes, King Crimson, Anderson Bruford Wakeman Howe, Earthworks

Nicko McBrain (UK, 1952- )
Style: Rock
Associated with: Iron Maiden

Sheila E. (Sheila Escovedo) (US, 1957- )
Styles: R&B, soul, funk, pop, Latin
Associated with: Prince, C.O.E.D., Ringo Starr

Carter Beauford (US, 1957- )
Styles: Rock, jazz, R&B, jazz fusion, world
Associated with: Dave Matthews Band, Secrets

Dennis Chambers (US, 1959- )
Styles: Funk, jazz, jazz fusion
Associated with: Parliament, Funkadelic, John Scofield

Mike Mangini (US, 1963- )
Style: Rock
Associated with: Annihilator, Extreme, Steve Vai, Dream Theater

Gavin Harrison (UK, 1963- )
Styles: Rock, jazz fusion, experimental
Associated with: Porcupine Tree, King Crimson

Jimmy Chamberlin (US, 1964- )
Syles: Rock, jazz fusion
Associated with: The Smashing Pumpkins, Zwan, Skysaw, the Jimmy Chamberlin Complex

Janet Weiss (US, 1965- )
Style: Rock
Associated with: Sleater-Kinney, Stephen Malkmus and the Jicks, Wild Flag, Quasi

Chris Adler (US, 1972- )
Style: Rock
Associated with: Lamb of God, Megadeth

Brann Dailor (US, 1975- )
Style: Rock
Associated with: Evisceration, Lethargy, Gaylord, Mastodon, Arcadea