If you like to have control over your images, Raw is the way to go. Some point and shoots have the ability to capture in Raw format. As far as I know, all DSLR’s can capture in Raw. Each manufacturer has its own format. You can tell what brand of camera was used to take an image just by the file extension. For example, Canon uses .CR2; Nikon uses .NEF; Panasonic uses .RW2, and so on.
The first time I shot in Raw, I chose the option JPEG+Raw, meaning that each image would be saved in two versions. That way, I would have the best of both worlds. To my surprise, when I looked at the set of images, the JPEG images looked better than the Raw. That is because the camera had already made the adjustments mentioned above to the JPEG version. It was up to me to make the adjustments to the Raw image, according to my style and vision. There are Raw Converters (software) specific to each manufacturer, but I prefer to use Adobe’s Lightroom software, once I have imported, tagged, and rated the images. The same functionality is included in Photoshop as Adobe Camera Raw (ACR), with a slightly different user interface.
To help illustrate the difference between JPEG and Raw, the following two images were taken from a single shot with the JPEG+Raw setting turned on. The camera was a Canon Rebel XTi. The original file size of the JPEG (on the left) was 3.8 MB, and the file size of the Raw image on the right was 12.3 MB. I brought each image into Photoshop and made a small selection in roughly the same area of each image. I did not make any adjustments to either image.