Don Henley was the Eagles' drummer. But it does sound to me like he used (better) session guys for his solo albums. Rhythm section work is a LOT better on those albums.
Does this include the many multi-instrumentalists out there? Prince, Adrian Belew, Steve Winwood, Lenny Kravitz...tons of folks that were/are competent drummers. Very few I'd call exceptional tho...
Gilmour also played drums on Fat Old Sun and The Narrow Way. Paul McCartney played drums on a lot of tracks on his solo albums and a couple of Beatles songs like Dear Prudence and The Ballad of John and Yoko.
Bootsy Collins plays drums on quite a lot of P-Funk stuff - and you have to be good to do that. This is the only clip I can actually find of him playing though:
Josh Homme of QOTSA plays drums with the Eagles of Death Metal, so I'm not sure he's a non-drummer. That's one for the philosophers...
More than a singer. He plays drums on every song, but doesn't sing on every song (or even close), not even on their first hit (Randy)
Mike Rutherford having a spirited crack behind a left-handed kit on everyone's favourite Genesis song:
Jaco Pastorius was pretty good on drums . . . and every other instrument I ever saw him goof around with. But unfortunately I never took any video--or even photos--of him playing drums and I don't know if any exists.
As far as I know. In a book I read it mentions Richard's more rudimentary style fitting some songs better.