My Fuji JZ500 (about $200) has 10X optical zoom, shoots video (blurry during zoom unlike the more expensive Panasonic).
It is discontinued but I'm sure they make an equal replacement now.
Fujifilm JZ500 14.1 MP Digital Camera 16008391 B&H Photo Video
The main reason I got this camera is that for it's type it does better than average in low light situations. However there is a setting which takes a low light picture, a mico-second later a second low light photo with flash automatically. This is a great feature, almost good as the 10X zoom.
The body is a little slippery, but overall I can recommend it as a simple point and shoot with bonus features. I've had mine for over a year with no problem.
Sample - I took this last spring: could not have gotten this close without the 10X zoom
