JPEG is definitely the most popular file format for storing photo files. Trouble is, how good it is depends on your camera.
JPEG is a file format which allows for the compression of the resulting file to save file space (i.e. removing part of the data). This is OK if done upto the point that real picture data is lost ("lossless compression"), beyond that you are throwing away part of your picture, which means you won't be able to print / view it as large as an uncompressed file, or a file that is only compressed so far.
Trouble is different cameras use JPEG differently. Some will compress all of the time; the better camera lets you choose the amount of compression, use lossless compression, or even use no compression (this is chosen on a picture by picture basis depending on what the picture will be used for).
So the disadvantage to JPEG, the most popular file format, is that you may lose quality of your picture.
Some cameras, like my Nikon's, have a special lossless J-PEG mode (Nikon calls it EXTRA). It automatically uses just the right amount of compression to save space, but not lose any of the picture.
The TIFF file format is the exact same way, you can choose the amount of compresssion you want to use. However many cameras don't support compression with TIFF, so you get a great quality, but large, file.
RAW is a file format that has VERY large file sizes, because it does no processing of the data from the CCD in your camera. All CCD data is written to the file.
The advantage of RAW is that you can get the most out of your picture with it after you have taken it, although you have to spend time processing it. For example, a person in a deep shadow of your picture may be dropped with JPEG or even TIFF, but will show up in the RAW file.
A good camera has more choices so that you can decide how you want the picture processed, based on what you think you will be doing with it (e.g. snapshot vs. poster).
Hope that helps.
CGB
P.S. I was just buying one of the new,cheaper, SMALL cameras, for a shirt=pocket camera, that still have all the features (8MP, vibration reduction, scene modes, etc.); I was disappointed to find that only JPEG is supported.