The first question: What are you going to be doing with the camera?
If you're taking pictures to email to people, and you're not shooting in low-light situations, or action situations, then just about any camera will do. Most people would prefer a small, compact, point-and-shoot camera, if their application is not very demanding.
If you will be doing a lot of action shots, or shooting animals, or wiggly kids -- things that just won't cooperate and and stand still, you'll need something that can focus fast. If you do photography in low-light conditions, or need a flash that can go more than 5 feet -- like up to 50 feet, then you'll need a camera that can support a good quality external flash unit. This is where a digital SLR, such as the Canon EOS Digital Rebel XT, Canon EOS 20D, Nikon D50, or Nikon D70s would be a good choice.
When I go out shooting for a day, I bring my Nikon D70, with 2 lenses, external flash, lens filters (circular polarizers are a must, if you shoot clouds, or go up to the mountains), spare batteries, and a spare memory card. And let's not forget the tripod. I'll easily shoot 300+ pictures in a day.
Of course, it's no fun lugging around that much stuff all day.
There are also some "advanced" cameras, that fill in the gap between the simple point-and-shoot cameras, and the digitall SLRs. The Canon PowerShot G6, Olympus C-7070 Wide Zoom, and Canon Powershot Pro1 fit into that category.
The best thing to do, is go down to a store, and try them out. Some cameras sound great on paper, and look cool, but you put them in your hand, and start shooting, and you might just absolutely hate they way they feel. Make sure you use a price engine like pricegrabber.com, to find the best deal. Many times, local stores will match internet prices.
-Tinytoad