Grant and Stewart are excellent answers. I think I would have to go with Cagney.
No nudity, no swearing, no graphic violence, no thanks. I don’t want to be stuck watching nothing but Hayes code era movies, and I won’t even mention the cheeseball acting styles.
Personally, I’d look for some bit actor that’s been in a billion different things. Quantity and variety is what to look for.
For me it’s Woody Allen or Al Pacino, easily. Forget about variety; I’d rather have a set of films with depth that I enjoy, than a set of films that span every genre possible.
Good call. Love Actually, Much Ado About Nothing, Wit…
Or maybe Dan Hedaya. He’s in everything!
Paul Giamatti. The movies he’s in aren’t high art (we’re talking stuff like Man On The Moon, Private Parts, and Shoot 'Em Up here), but they’re almost always guaranteed to be entertaining.
ETA: Looks like he was in Saving Private Ryan, so there’s your high art war movie. 
The slap fight between him and Tom Wilkinson in Duplicity made it all worth it!
… and Shane.
Ben Johnson, Robert Duvall or Paul Newman for me. Tough choice.
Bolding mine. I totally got a visual of that sentence.
Also, second the De Niro nom. Is he senile? I wasn’t aware of that.
Gene Hackman and Robert Duvall are the actors that first occurred to me.
My pick.
For dead actors, Bogart or Robert Mitchum.
Wait, wait. Instead of Giamatti, I gotta go with Ron Perlman. He’s got some stinkers, but on the whole he’s just great to watch. And it also means I get some Guillermo del Toro movies in the lineup.
Dick Miller or possibly Gene Hackman.
Serena Grandi http://www.greencine.com/webCatalog?id=20613
… and a giant mythological rabbit!
Match that, Hanks.
I smell a loophole… does he have to actually be in the movie? Or does directing or producing count?
I’d pick Brad Pitt. I haven’t seen a movie of his I didn’t like (but then again, I never watched The Mexican), and he’s still making them.
For once, Diogenes and I are in total agreement. I can’t stand to watch the same movie twice in about a five year period, if not longer. That’s why I don’t own many movies: I rent, watch everything on the disc, and then I’m done.
Rucksinator’s loophole is interesting, though. In fact, the best choice would be a some unknown actor who just happens to own copies of every movie I’ll ever want to watch (or who I can pay to buy movies I want to watch) who will loan me copies. Then I’d be “watch[ing] one actor’s movies,” wouldn’t I? 
Klaus Kinski. I’m sure a lot of his films are horrible but there are a lot of them, and I always enjoy watching that unique … madness … he brings to his characters.
Charlton Heston
Gerard Depardieu
Richard Burton
Max von Sydow
Sean Connery
I’d go with Mel Blanc.
He has over 700 movie credits to his name. I’d never get bored that way! 
Since “Snatch” is my favorite movie right now (for the last few years, actually) I’ll have to go with Brad Pitt.
The other actor I thought of is Paul Newman. Films from the 50s until his death.