All depends on why the character is being recast: I don't have any problem if it's for a younger version or something of the like (as long as the new actor is not too different in appearance). But if there's nothing to justify that decision, then I think it's better to just switch the character for a different one, because it can be a real damper otherwise.
And I have, in fact, a quite illustrative example in the Lars von Trier's never-finished trilogy consisting of Dogville and Manderlay: I rewatched Dogville just to have it fresh in my mind before watching its sequel and, when the next day I saw that the main character didn't look even remotely close to the one in the first part (in spite of supposedly being the same person), I felt completely off the movie. And the worst part is that this director has made other trilogies that are linked by their theme, rather than their stories or characters, so why on Earth didn't he just do the same here? Maybe it was a last minute issue and they couldn't change the script or something like that, but heck, I didn't enjoy the movie near as much as I could have just because of that shit (the movie is good, by the way, which only makes this situation worse).
I'm mostly a lurker now.
