There's also:
Michael Dorn who has a Sabreliner and previously owned an F-86 and T-33
Aaron Tippin (who's more of a singer than actor) who has a PT-17, SNJ-4 (Navy version of the T-6 Texan), and is a pilot for the CAF on their B-29 and B-24 in addition to a Cub and a Cessna 421
Lorenzo Llamas has/had an L-39 and a Pilatus PC-12
Jimmy Buffet has several airplanes including a PT-17, HU-16, and a Grumman Goose. The Goose may be familiar to most of you as it's the plane which the FSX Goose is painted like -
http://www.buffettworld.com/aviation/goose/ (although he bought it after MS made the paint scheme "famous")
There's a few others who don't own warbird like:
David Lee Roth (helicopter rating)
Sydney Portier (has a Learjet)
Clint Eastwood (and his son Scott) both have Helicopter ratings
Morgan Freeman used to have a light twin, but I'm not sure he's still flying
Dennis Quaid has his private and multi-engine ratings and at one time had a Beech 18 and also is type-rated in the Citation
Chuck Woolery has his Private/Instrument rating, don't know what he flies/owns though
Cliff Robertson had several planes over the years including a couple of Cessna Twins
Fess Parker (aka Davey Crockett and Daniel Boone) had several single engine light airplanes
Patrick Swayze owned several airplanes
Kurt Russell at one time had a Cessna 402
Roger Barnes (better known as wrestler Ron Garvin) had a DC-3 for a while, don't know if he still has it though
We don't hear much about most of them mainly because their job means that they usually can't fly while they're making films (although Harrison managed to get approval to do most of the on-film flying for the movie "Six Days Seven Nights", which is where his Beaver came from - he bought it from the Studio after the filming wrapped - full story
here).