Mary Poppins [SPOILER ALERT] is a good example of this type of character. She doesn't change, but she has a profound effect on Mr. Banks and, in doing so, improves the life of the Banks children.
Forrest Gump is also a character that doesn't change. No matter how dark, serious and complicated the world around him gets, Forrest retains his simple outlook and sense of hope, which influences the people around him and makes their lives better.
I started this series by saying that war movies don't usually involve arcs, but "Mister Roberts" is one exception. In the film, [SPOILER ALERT] Mister Roberts (Henry Fonda) doesn't change, but his bravery in standing up to his tyrannical captain (played by James Cagney) and his ultimate sacrifice to do what he feels is right have a huge transformative effect on Ensign Pulver (Jack Lemmon).
It's interesting to note that in all three of these cases where the main character is the agent of change the title of the film is their name. Some people refer to these type of movies as "traveling angel" movies (I believe Blake Snyder coined the term).
Ferris Bueller (from the movie "Ferris Bueller's Day Off", of course) is another example [SPOILER ALERT]. Ferris doesn't really change, but the day that the two of them spend together has a profound effect on Cameron, who arcs from someone who is scared of his father and intimidated by him, to someone with the guts to stand up to his father.
Sometimes, in these types of movies, the main character is bent upon obtaining a goal and they drive towards that goal with unflinching determination, even as people tell them they'll never be able to achieve their dream. Their passion and resolve inspires people around them as they try to reach their goal. At some point, the character loses their drive and passion and questions whether or not they'll ever realize their objective, and even start to think that they were fools to undertake this journey in the first place. Right at the moment that they're considering giving up, someone that they've inspired along the way comes along and re-inspires the character and gives them a renewed sense of purpose, which re-ignites their drive.
"The Muppet Movie" follows this kind of structure, and I'm pretty sure the film "Rudy" does as well (but it's been years and years since I've seen it, so I'm not 100% sure that's correct).
One of the things I liked about working on "Tangled" [SPOILER ALERT] is that it has a bit of an unusual structure - it has both types of characters: one that undergoes a personal change, and one that changes the world. Rapunzel doesn't necessarily go through a big change - in the end, she realizes that her life is an entire lie, but that doesn't involve an emotional change in her psyche, that's more of an external change in how she perceives the world. She's more of the kind of character that has a positive effect on the world: she transforms the people she meets along her journey, and by returning to her parents at the end, she rejuvenates the kingdom.
Flynn has more of a traditional arc: he goes from being a larcenous thief who doesn't care about anyone else to someone who changes his priorities as he falls in love with Rapunzel, and eventually realizes that she is more important to him than material possessions.
James Bond is a character who has a big effect on the world in every movie in which he appears. He's constantly saving the world from being destroyed or taken over. He doesn't really have much internal transformation, though. Clearly, his internal landscape is not what the films are about, and anyway, it would be odd to come up with a different emotional arc for him in every film. After a few films he would start to seem like a strange, overly sensitive and wishy-washy person with constantly shifting emotions. Also, it would be confusing if you watched the films out of order. His personality would be at a different point in each movie and he would seem completely erratic and inconsistent as a character.
This is why, traditionally, TV shows don't really change the characters that much either. You can't rely on viewers to watch a show from the first episode and watch every episode every week, so you can't really arc the characters, because it would be completely confusing if you miss an episode or watch the shows out of order. Traditionally, sitcoms are trying to create enough episodes to reach syndication, where the episodes will be replayed in infinity (but not necessarily in order), so it would be really strange if the characters were constantly evolving and changing in every episode. The characters you've come to know and love wouldn't be the characters you'd fallen in love with....they'd be a different person every week! So once shows find an archetype or personality that can generate humor and connects with an audience (Bart Simpson, Kramer, etc) they'll mine that character for as long as possible. If anything, the rule seems to be that the longer a show runs, the more the characters seem to get more and more one-dimensional and become reduced to a few character traits.
When it comes to dramatic one hours shows (things like "Law and Order"), it seems like the characters are consistent every week and the "change" within the story is whatever crime that's set up and solved within that week's episode.
Even if you tried to create a series of movies or a TV show where the character had a big emotional arc every week, it would start to feel completely insincere after a while. If you can have a big emotional swing every week, how deeply seated are your emotions, anyway? In any transformation, whether it's a character changing or the entire world changing, it ought to take an enormous amount of effort to affect the metamorphosis. People don't change lightly and, as we all know, it's not easy to change the world. The most dramatic stories are the ones where a change only takes place after much struggle, effort and conflict. Change should never come easy, whether it's internal or external. Change that comes easily to characters is not very interesting, compelling or inspiring to watch.