I have the Canon Powershot SX260 here which is under $250 now. It takes HD movies at 1080p, has a 20X optical zoom, and is very compact. I've gotten some beautiful pictures from it.

Overall I'm very happy with it, I've had it for 2 years and it's survived multiple hikes, bikes, vacations, pockets, purses, and kids handling it. Only issue is that the flash pops up where you tend to put your left hand, so you have to get used to holding it differently. And I've found the "scene" mode on portrait is better than the "auto" mode in a lot of cases.