Barbara Stanwyck.
I was surprised that ANYone picked an actress, as the OP said “actor.” I took that to be the challenge.
I’d go with Daniel Radcliffe. He’s got a long career ahead of him, and seems to pick scripts with an intellectual or philosophical twist to them. And he doesn’t seem to want to just hang about now that he’s got all the money he could need. So I’d be likely to have a long life of at least intriguing film ahead of me.
I don’t understand picking someone whose career is over, or nearly so. Why damn yourself to a life of re-runs?
Alan Rickman
I’m sticking with that one-name actor that has been in such a wide variety of movies over so many years, sometimes even play two, three, four (or even more!) rolls in the same movie. This actor is capable of playing any age, ethnicity or sex, and do so without flaw.
Unknown.
Niven, Caine, or Katharine Hepburn. It’s a hard choice…
Susannah York. Starting with Sebastian, of course. Lots of good movies in the 60s and 70s. And if I got real desperate there’s Superman and Superman II.
Speaking of which, there’s always Vic Armstrong. 
Samuel L. Jackson
Not necessarily because of him or his roles but because he’s in such a variety of different films that I like. All the Marvel films, a bunch of Quentin Tarrantino stuff, The Incredibles, Jurassic Park And Kong, Goodfellas, Patriot Games, DieHard3, etc.
Nicolas Cage.
What can I say, I like bad movies, and Mr. Cage apparently will say “yes” to literally any script. There’s a handful of legitimately high quality fare peppered in there, e.g. Raising Arizona, Leaving Las Vegas, Adaptation, etc. There’s also a whole lot of genuine shit, but again, I like that. And the man has managed to hit nearly every conceivable genre throughout his career, so at least there’s a wide variety of shit.
The word actor is gender neutral
- A person who behaves in the manner of a character, usually by reciting scripted dialogue, in order to entertain an audience, especially in a play, movie, or television show.
Alec Guinness!
My son informs me I’m required to admonish you that friends don’t let friends watch voice dubs. Must admit that, on the whole, I agree with him.
(Right now he’s checking which voice actor in Space Brothers he can tie to the largest number of other favorite anime, albeit the OP specified favorite actor to watch, which kinda rules out voice only, as well as movies, which leaves out TV series.)
Another vote for Cary Grant…
Peter O’Toole
That’s easy…Pez. Cherry-flavored Pez: No question about it.
^ Sugar overload!
If I’m following the spirit of the thread, maybe Kurt Russell. Gary Oldman was a good suggestion too.
If I’m being practical, maybe Madison Ivy?
What, no love for Harrison Ford? His box office numbers are insane!
Now, I could use more small, complicated movies than what he generally supplies, but I almost always have fun at his movies, so I could live with only seeing his stuff.
Most of those are barely worth watching once, let alone over and over. Looking at IMDb I count 3 of his movies that are worth watching a few times and only one, Blade Runner, is worth watching many, many times. (Especially if you get to watch all the different cuts.)
He is in a few other really good movies as a secondary character. E.g., The Conversation, but that was a looong time ago.
Michael Caine FTW.
Yes, he’s been in a fair number of stinkers, but I think I’d take a long time to get tired of re-watching:
Inception
The Dark Knight
The Prestige
Children of Men
Noises Off…
Hannah and Her Sisters
Dressed to Kill
The Eagle Has Landed
The Man Who Would Be King
Sleuth (1972)
Get Carter (1971)
Battle of Britain
The Italian Job (1969)
Billion Dollar Brain
Funeral in Berlin
Alfie
The Ipcress File
Zulu