I am a big fan of digital photography. One of the questions people ask is which camera to get. The answer is that it depends on the photographer and the environment where you photograph. The biggest question is whether to get a digital SLR or P&S. I am not covering that decision in this discussion.
Wen it comes to P&S cameras, the first question you need to decide is how much manual control you want. Some cameras offer many manual control options like shutter speed or aperture. Some people care about and want to manually set these options since it provides more flexibility and creativity. Typically these cameras that offer manual features also offer full automatic and so you don’t always have to monkey with the settings. However, the trade off is that cameras with more manual features are typically larger in size. Thus, the choice is between small size and portability with a bit larger size and more flexibility. Here are a couple of examples with links to listings at Amazon (Note that I am a Canon guy and so these are listings for Canon cameras, all the other manufacturers offer cameras with similar features.)
Manual Camera: Powershot G9
Automatic Camera: Powershot SD870
The choice betweent these two types of cameras comes down to the user. Are you more interested in the best image quality, configuration flexibility and are willing to sacrifice some size for these features or are you more interested in having a very small camera where you simply just press the button with little or not user interaction. The choice comes down to user preference. I personally prefer the former because I enjoy manually changing camera parameters.