Characters
I think characters that grow and change can be good, but I also think such things can be, and often are, taken too far. Much too far.
A character who learns from whatever the story throws at him is good, but changing can sometimes be a bit much, if handled poorly. If you have a character readers like, then why change him. If you have a character readers don't like, are they going to stick with him long enough to see him change.
Major changes in character often work better in secondary characters of villains.
Learn and grow, yes, but take a look at some of the more memorable series character of the past. Sherlock Holmes, Travis McGee, Spenser, Sam Spade, Philip Marlowe, etc. Read book one and book last and see just how much actual change there is in the character. They do grow, they do learn, but they don't change much at all.
The story where a truly rotten guy turns into a wonderful person, or a guy doing all the right things turns into something evil have their place, but it can get old fast.
So can the story where a guy starts out hating this or that; blacks, gays, ketchup on hot dogs, etc. This sort of story works better than the former, but it's also prone to manipulation, and doesn't always come across as anything other than a lesson in morality.
And so many changes writers put their characters through are cliched almost beyond usability. The first one that comes to mind is the hero who is out to avenge someone, and cuts a swath of blood in the process. But when he gets to the last guy who needs killing, he's had enough. He doesn't want to kill anymore.
For me, creating characters who are human, and who actually act human without me manipulating them into unnecessary or unbelievable change works best. Most changes in real people are subtle, and even the big changes usually take place over a long period of time. In real life, change is usually a process, a long one, and very often isn't change at all. It's just a matter of bringing to teh surface what was always underneath. I'm not the same person I was twenty years ago, but I haven't turned into someone else, either.
I think "Live and learn" is a good rule with characters. But "characters must change" can be more than a bit much, and flies in the face of some of the more popular fiction ever written.
As for sympathetic characters, I think sympathy rests squarely on the shoulders of motivation. I need to be able to say, "Yes, that's how I would react." Or, "I might not react that way, but I fully understand why he does." If this happens, I'll have sympathy for the character.
But the moment I say, "That reaction is over the top," or "I'd never react that way in a million years," or the real killer, "For God's sake, get over it," that character has lost all sympathy I might have had.