In most novels and screenplays, your protagonist undergoes a change over the course of the story, and that's called the character arc. In most Hollywood films the change is from some kind of negative state (self-centredness, insensitivity, greed) to a positive one (concern for others, ability to love, generosity), as in "A Christmas Carol." Not always, though--consider the arc of Michael Corleone in the "Godfather" movies.
When the arc is handled well, it seems natural. However, there are three common problems that can make a character arc seems clumsy:
* When the size of the change doesn't match the size of the incidents that supposedly cause it. If a character is consumed by greed, one conversation with a beggar isn't likely to make him suddenly become altruistic. We know from our own experience and observation that it usually takes a big event to cause a big change. If you've ever seen that list of the things that cause the most stress, it's a pretty good guide: a near death experience, losing a loved one, a serious illness, divorce, losing your job, etc. If you want your character to undergo a big change, your story has to give him big kicks up the backside. Usually several. Remember, Scrooge required three ghosts, not just one.
* When the change is one-dimensional. Let's take a male mid-life crisis as an example. Yes, one obvious change might be that he buys a red sports car, but it will also be reflected by all kinds of little changes as well. These might be getting a new hairstyle (or a toupee, or hair implants), a change in what he wears, joining a gym, and so on. I'm not suggesting that you have to include all of these. That would be overkill. But you'd definitely want to have this change reflected in several ways, and if you can find some more subtle ones, so much the better. Each of these would also have an effect on the character's relationships, so we want to show those ripples as well.
* When the change is too easy. We humans have a hard time changing. Seldom is the path smooth (and of course smooth paths don't make for interesting drama anyway). There should be setbacks, unintended and unanticipated by-products of the change, and retreats.
It may be that we enjoy watching others change because it's easier than changing ourselves. When the character arc is well motivated and realistic, it becomes a great driving force for the story.
(For more tips on characters and plot, see my book, "Your Writing Coach," published by Nicholas Brealey and available from Amazon and other online and offline retailers. More details at www.yourwritingcoach.com)