I have a Canon Powershot A20 that I purchased several years ago. It is still going strong. My advice is to think about the kinds of pics you will be taking with the camera and what you will be doing with the photos after they are taken. Then, choose the camera that fits your needs.
In general, More megapixels = better quality = larger file size = higher price. If you are gonna print out 8x10 photos, you'll want to get something with decent resolution (high # of pixels). If you are only gonna download them to your computer and e-mail them to family, you can probably live with a 2 or 3 megapixel camera. I can get good 5x7 photos with my 2 megapixel camera.
Optical zoom is better than digital zoom. Get something with good optical zoom if you are gonna rely on the zoom a lot.
When using a digital camera, there is a pause between the time the camera takes the photo and when it is written to the memory. This is called latency. If you are going to take lots of action photos (kids playing sports, etc), you may want to think about a camera with a low latency value.
There are lots of media (memory) choices. Sony has the media stick, others use compact flash, etc. I personally am not a fan of the ones that write to a floppy disk, though some people like the ease of transferring the photos to the computer. Your gonna be limited to how many pics you can store on a floppy. Anyway, the camera will come with some memory, but you almost always need to purchase additional memory if you are taking lots of quality pics. My camera uses compact flash. It came with 8MB, but I purchased a 128MB card. I can take over 200 pics at the highest resolution, 400 with medium resolution. It works great for vacation pics. No more film!
OK, enough rambling. For more research, check out:
www.activebuyersguide.com
^ this site is good for helping you choose a camera and understand all the technical options that come with the cameras
www.epinions.com
^ this site is good to read reviews of people who purchased cameras (and lots of other stuff) and their thoughts on the product.
Anyway, good luck.