You looking for a small, easily carried point-and-shoot; a "medium" camera with more manual features and a lot of zoom; or an SLR?
As brands go, stick with the reputable ones...Sony, Nikon, Canon, and Olympus are my top four. Fuji is okay, as is Pentax, but do yourself a huge favor and avoid all things Kodak, GM, HP, Sanyo, Samsung, etc. Kodak Easy Shares are especially crappy, though favored by the unknowing, and elderly.
If you're looking at point-and-shoots, take a good look at what Sony has to offer. I have the WX1, and love the thing (auto bracketing, 10 shots per second at full res, and Sony's hand-held twilight mode). Sonys have great low-light performance and excellent color balance. The W330, W350, WX1, TX1, and HX5 are all great and go from $170 to $399-ish. Canon also has some good cameras, like the S90.
Next up you have your super zoom cameras, which are essentially point-and-shoots but with a lot of zoom. Many also have SLR-like options, like shutter priority, aperture priority, and manual modes, which are very helpful. The Sony HX1, Nikon P100, and Canon SX20 are all ones to look at in this category. I have the Canon SX10, also, and think it's a great camera. I especially love the three-stop auto bracketing.
Then there's your SLR cameras. These offer the best image quality (owed to their larger image sensors) and most control-ability. Prices range from $400 for the Nikon D3000 to $38,000 for the Hasselblad H4D-50 MS (drooling right now). The entry level cameras are pretty reasonably priced, but the extra lenses are what can drain your bank account...fast. A good lens can run you anywhere from $140 for a Nikon 50mm f/1.8, to $600-ish for an 80mm f/1.8, to $10,000 for a 600mm f/4 VR. The Nikon D90, Sony A500, and Canon T2i are some good options, here.
Finally, there's the newest category, Micro Four Thirds cameras. These are like mini SLR cameras. They often have a nice old school vibe, aesthetically, and offer the flexibility of an SLR camera in something as easy to use as a pocket sized point-and-shoot, all in the size of a super-zoom camera. It's still an emerging class of camera, but I think it's going to grow a lot in the near future. The Olympus E-PL1 and a good example of this class of camera, and runs about $599.
Also, more photos!