I've been a huge fan of the Canon Powershot IS series, since I discovered it several years ago. I've owned the S2 IS, S3 IS, S5 IS and now the SX10 IS. They run around $300 and have an incredible optical zoom (20x with the SX10 IS), image stabilization, and a great video shooting option (640x480 at 30fps). It uses SD cards and AA batteries, which I really like. We use rechargable batteries in it. You get several hundred pictures per set of batteries. It's a bit bulky, but it takes excellent pictures and you can really reach and a get good pictures of distant objects.
I'm not sure if it's from design issues or excessive use and abuse on my part, but each of mine has only lasted around 2 years. It has a 1 year warranty and we have always bought them with our American Express (which doubles warranties up to a year), so it's worked out good. Two broke shortly before the doubled warranty was up, so we got full refunds which we used to buy our next ones. The S5 IS lasted about 27 months, so the string of free upgrades stopped. The SX10 IS has a slightly different design which I think might fix the problems, and it's a significant upgrade from the previous models.
I know many people like a smaller camera that will easily fit in a pocket or purse, but if you're looking for a larger, more powerful one, I can't say enough good things about the Canon Powershot SX10 IS. We love ours.