It depends on your price range. I’ve been very happy with the Fujifilm Finepix F10 because of its good performance in low light and long battery life. If it ever dies, I’ll buy the sequel the F30. I’ll spare you the details of why not the F20, F31, or F40. The F30 plus a 2GB xD card will cost you about $400, but you’ll be able to take very good shots.

5 to 6 megapixels is sufficient for most users. Most cameras are 3X optical zoom and 4X. Others are 10 and 12X optical zoom. The more zoom the more it costs.Some cameras eat up batteries quicker than others. A very good compact camera is the Canon PowerShot A630. It has 8 megapixels, and 4X optical zoom. Excellent on AA rechargeable batteries.
Another camera I’d consider is one which I own that has plenty of zoom is the Sony Cybershot DSC-H2. 6 megapixels, and 12X optical zoom. Has image stabilizer. takes excellent 8X10s when enlarged. Very good on batteries, comes with batteries and charger.
The Canon can be had for $191 at Beach camera, the Sony about $300- in most stores. Check out Website dpreview.com for reviews of cameras and prices.

More megapixels mean greater resolution – in general this might translate to a better quality picture, one that you can blowup to a bigger size without loss of detail. In your case you’ll probably consider factors such as portability (lightweight and can fit in your pocket or purse), decent picture quality (maybe 5 MP), and ease of use (point-and-shoot).

If you’re taking lots of pictures and recharging batteries could be a problem – long outdoor trip or vacation to a place with different power suppy (Europe or such) – you should consider a spare battery or get a camera that uses regular batteries that are readily available.

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I’ve been looking at a lot of Canons in the SD series. They’re mostly small and very good cameras. For any kind of photography now-a-days you need 5 mega pixels or more. I’m getting the canon sd750. It’s about $260 on amazon.com and I’ve read a lot of great reviews for it. It’s small and has the “face detection” technology. There’s also a setting called “kids and pets” that seems to focus better while subjects are moving. My favorite feature though is “color accent” where you can pick a certain color to stay, while the rest of the photo is black and white. Good luck!