Avoid HP and Samsung digital cameras. HP couldn't make a camera to save its life and most Samsungs flashes go out within a year or so.
As CG said, its all about zoom and quality of picture. A higher quality camera (8 MegaPixles and above) tend to be good still photo shots, but will take up more storage on the memory card.
Try to avoid having a Lithium-Ion battery camera. Once the battery is toast, you might as well just buy yourself a new camera.
As far as brands, I'd go with this:
Canon/Nikon*
Sony
Fujifilm
Kodak
Olympus
Samsung
HP
Depending if you get an SLR, Nikon all the way, followed by Canon and Olympus.
Watch out for Sony. They like to be different with there memory cards, just make sure you buy the right one.