best movie where an actor plays more than one character.

I agree with your pick of Dr Strangelove.

Not a movie, but Tatiana Maslany is absolutely brilliant in Orphan Black...

The Mouse That Roared (1959)
Another Classic Peter Sellers.

It depends on what you mean by "best movie" and whether you're rating the film based on the film's strengths or based on how well the actor takes on multiple roles.

Let me start by saying that your choice of Dr. Strangelove sprang to my mind immediately, and somebody else on the boards mentioned Adaptation, which is top-grade, as well. Here are my contributions:

I'll add Monty Python's films to the growing list. My personal favourite is The Meaning of Life, but I know for most people it's The Life of Brian.

If you count the Lord of the Rings trilogy as one, big film, then I might go with that (John Rhys Davies and Lawrence Makoare double up at various points in the trilogy). Technically, they're multiple films, but they are one story.

The Muppet Movie features Muppeteers working a whole slew of characters each, and it's excellent. Who doesn't love the Muppets?

Those are the ones that spring to my mind, anyway.

The Parent Trap (1961) - May not be the best but one of my favourites.

LEAVES OF GRASS (2009)

Trilogy of Terror 1975

Jim Carrey A Series of Unfortunate events