Mike Portnoy gives his influences in this excerpt from a Daily Vault interview:
I used to like Neal Peart but I don’t really listen to him that much anymore. He was a big influence for me when I was younger. I really listen to so many different drummers I mean, Terry Bozzio, Simon Phillips, but when I listen to music I don’t really listen to the drummers… I listen to the ways the songs are produced, I listen to the ways the songs are written. When I listen to music there are lots of aspects I listen to, not just the drummers.
In a more recent Sabian Q/A session, he answered the following:
Sabian: Your favourite drummer in today’s music scene?
Mike: Mike Mangini, Vigil Donati, Marco Minnemann, Danny Carey, Carter Beauford
Sabian: Who, in your opinion is the Drummer of all drummers?
Mike: Vinnie Colauita
Sabian: The Pioneer?
Mike: Terry Bozzio
Sabian: The Legend?
Mike: Ringo Starr or Neil Peart
On his website the following is written:
Mike says his biggest influences are Rush drummer Neil Peart and the late Frank Zappa. Other favorites include drummers Terry Bozzio, Vinnie Colaiuta, Simon Philips, John Bonham and Keith Moon and bands such as The Beatles, Queen, Yes, Metallica, Jellyfish, Iron Maiden, U2 and Jane’s Addiction. He is also a fan of rap music.