S. Boyd (Sam) Taylor dropped a comment on my previous post, noting that a teacher once told him that if your protagonist didn't change, you didn't have a story...and that he'd been looking for a good counter-example.
I think there's plenty of counter-examples. Many of the Greek myths, for example, feature iconic characters who never change.
Well, a lot of them end up dead, which I suppose is a change, but very often they persist in being the same people up to the point where they stop breathing. And a common element in classical tragedy is a protagonist who doesn't change, and therefore circumstances around him change--usually in a way he dislikes. (And then he or she ends up dead, too.)
A lot of them who end up dead also end up as constellations, which I suppose a lawyer could argue is one of the biggest changes you can imagine. But most of these constellation-people were unchanging in life, and, up in the sky they remain icons for the forces they personified. Take Hercules--does he have a character arc? C'mon.
(I'm not saying all mythological characters lack arc. Gilgamesh, for example, learns many things in the course of his epic, and his outlook on life is transformed.)
And we don't need to retreat to ancient myths. In Fleming's novels, James Bond never really changes; neither do many superheroes in comic books. (In fact, superheroes who do change were considered to be a revolutionary step in the early days of Marvel Comics.)
One of the entertaining things about the "reboot" of the James Bond franchise in the movie Casino Royale is that the Bond of the movie isn't yet the James Bond we know, as illustrated in the hilarious (to Bond aficianados) exchange:
BOND: Vodka martini.
BARTENDER: Shaken or stirred?
BOND: Do I look like I give a damn?
In Casino Royale, for once, Bond has an arc. He starts as a chilly but impulsive don't-give-a-damn type. Toward the end of the movie, love makes him begin to open up to life. But then all his hopes are destroyed, and in the very last scene we have the Bond we know: closed off, smug, and transformed from chilly to solid ice. But this arc is a Just-So story, like How the Elephant Got His Trunk. It's all in service of explaining how someone became the ever-unchanging Bond.
Some people latch onto the Bond/superhero examples to assert that unchanging characters are inherently two-dimensional or cartoonish. I don't think this needs to be true (Broadcast News has complex, three-dimensional characters)--at least not for the length of a single story. Unchanging characters can be perfect guinea pigs to conduct that experiment for which novels are the greatest laboratory: What is the result of a particular unyielding personality type and worldview encountering life?
On the other hand, if you have a series character who never changes--like Poirot or Holmes--they are bound to feel cartoonish when we see them in book after book. This may be why Conan Doyle was constantly adding character traits, such as cocaine addiction, to Sherlock--they helped round out a character who wasn't growing across time.
You can argue that unchanging characters are usually less interesting than characters who are changed by events, and I wouldn't disagree. But to argue that unless the protagonist changes, you don't have a story, is just silly.
I mean, really: Did Noah have an arc?
[The answer, incidentally, is 'no.' For 600 years before the Flood he was the most righteous and upright of men, and for the 350 years he lived after the Flood, he was...well, the most righteous and upright of men. No arc.]