for me, secondary na lang yung MP count, since 4 MP and 5 MP are more than enough to print short bond paper-sized prints. image noise levels tend to increase as megapixel count increases too, in general, unless you're looking at dSLRs. plus, you lose more detail in downsampling 8 MP images to smaller sizes than in downsampling 4 or 5 MP.
besides size and weight (for an everyday-carry camera), una kong titingnan yung quality ng lens -- sharpness, color, and speed (f/2.8 is standard, smaller number allows higher shutter speeds, which is VERY useful, larger number means longer shutter speeds, which is VERY bad for handheld shooting). reviews on the net are very helpful in that regard. other considerations are battery life, LCD screen quality, storage media type, and battery type.
wide-angle lenses (mga 28 mm. equivalent) are VERY useful, as is an ultrafast lens, like the f/1.8 lens on the olympus C-5050Z, or the f/2.0 lens on the Canon G3, G5, and G6 and the Sony F717 and F828. i don't find long zoom ranges very useful in everyday shooting