For general digital cameras there are 4 main things
1) Highest number of megapixels you can afford (about 4 or 5 is standard nowadays)
2) An OPTICAL zoom lens (not a digital zoom lens)
3) A Lithium Ion battery (not AA or AAA which forever need re-charging)
4) A good quality lens.
I would also go for a good camera make (Nikon, Canon etc). These companies got big by providing quality products.
I am not saying every camera they make is good, but you are better off getting a Nikon or Canon than a no-name brand from your local supermarket or Argos.
This site is great for reading camera reviews
http://www.steves-digicams.com/
He also gives his best buys for each type of camera
http://www.steves-digicams.com/best_cameras.ht ml
Note it is an American site so some cameras may not be available here, or have a different model number.