Previous related threads: here, here, here.

Repeating my previous answer:

Luna from Harry Potter displays a Stoic personality as well as any character I have thought of.

Why? Because instead of merely not letting her emotions (passions in the Stoic technical sense) show or interfere with her choices, she seems to find genuine equanimity by actually avoid having them at all through not judging externals bad. For example, she doesn't merely endure the mockery of her peers; she doesn't seem to mind it enough for there to be anything to endure. Her situation is as bad or worse than most of the main characters, and yet she maintains equanimity throughout.

Also, Hannah Jelkes from The Night of the Iguana seems like a good example of a Stoic attitude.

For example:

Maxine: You're completely broke, are you?

Hannah: Yes, we are -- completely.

Maxine: YOU say that like you're proud of it.

Hannah: I'm not proud of it or ashamed of it either. It just happens to be what's happened to us.

There are a number of other similar instances. The circumstances of her life and the things that happen in the story are as bad as that of any other character there, and yet she handles herself far better.

Holowchak's use of her as an example is what prompted me to watch the movie at all.

Cordelia from King Lear was, I think, deliberately written to exhibit a somewhat Stoic kind of virtue.

In addition to these previous answers of mine, I agree that Captain America is a good example as well.

Examples commonly mentioned by other include Spock, Snape, and the man with no name, but I think these are closer to the common misunderstandings of Stoicism than historical Stoicism; the calm rationality in these cases seems more forced than naturally arising from a sagely perspective, and none exhibit the natural affection cultivated by the Stoics.