So far no one has (seriously) listed Phil Rudd, Meg White, Moe Tucker or Chris Franz
I find this question hard to answer honestly. It depends on the period of my life and the music I'm playing at the time. When I started it was all Ian Paice, John Bonham, Aynsley Dunbar,, Bill Ward and Roger Taylor. Then Mitch Mitchell, John Densmore, Ringo and Charlie.
Later I was in the thrall of prog/fusion guys like Bill Bruford, Carl Palmer, Billy Cobham and Steve Smith.
Then it was session players like Steve Gadd, Rick Marotta, Jeff Porcaro, Purdie, Jim Hodder - basically the Steely Dan guys. Also Danny Seraphine.
I also saw a lot of local jazz hotshots who played in bands with my sister's partner. Not to mention all the bar band players.
In the 80s I had to completely change my style so as not to sound dated. I looked to players like Chris Franz (he was one of the few drummers around at the time playing a purely acoustic kit in 80s music) and Jon Farris from INXS.
Lately, I've been listening to jazz players because I'm trying to develop a jazz touch (not technique, that's another planet) because I'm in a laid back band but don't want to sound like a dead fish. I've also paid much more attention to other women drummers, who were never on the radar in the old days.
If I was to look at which influences stuck the most, I'd guess:
Bonzo - who left an indelible mark, whether I like it or not
Bruford - for inspiring me to look for options outside the square and to embrace bright kit sounds
Steve Gadd - for his ghost notes and flowing feel
Meg - for helping me overcome the fear of simplicity (though I could never be
that simple for more then a few bars)
The other spot would be filled by a mix of all the above players, plus a whole bunch of people I've probably forgotten, including many relatively unknown local drummers. They are all better than I am ... I always feel like
everyone plays better than I do and it surprises when people say they like my playing. All I see are the myriad flaws and limitations. In the end, I just try to fit with the music and whatever comes out, comes out ...