Lots of posters above recommend expensive cameras like DSLRs (>$600) or the Canon S100 ($430). My advice would be that the best camera is one you can carry with you, and that you can use easily. All of the major brands produce cameras in the $100 -- $150 range that will take excellent pictures. The current level of specifications for these cameras is easily illustrated:
"For $91, Nikon Coolpix L22 has a 3.0 inch LCD display screen, 12.1mega-pixel sensor, and 3.6x zoom lens (35 mm equivalent 37 â" 134 mm). Its features include built-in electronic Vibration Reduction and Motion Detection, Scene Auto Selector and Easy Auto Mode. It will fit in your pocket and weighs less than 7 oz. Powered by AA batteries, easily available anywhere."
I found the above information at DPReview.com which has some terrific comparison tools as well as detailed reviews of many brands and sizes.
The most important part of photography is not the camera but the eye, the mind, and the heart of the photographer. Learn about lighting, perspective, and composition before you worry about gizmos.