Reprinted from Good Gear Guide

JPEG: The universal format

If there were a universal file format for digital photos, it would be JPEG. Every digital camera on the market today shoots in JPEG. It's not hard to see why: The format is readily recognized by every computer and every photo program in the universe; and the files are reasonably small, efficient, and of high quality.
What many people don't realize, though, is that using the JPEG format is somewhat destructive to your images. JPEG uses a "lossy" method of file compression, unlike a method such as Zip that involves no loss of information. This means that JPEG discards small amounts of color information when you save an image; the original JPEG created by your digital camera starts out as a close-but-inexact replica of what you saw in the viewfinder. That's hardly a problem in most cases, as your photo still looks accurate because there's sufficient information to please the eye.
The problem arises when you save a new version of the file in your favorite photo editor. Every time you save a photo in JPEG, the file gets compressed a bit more. The effect of this process reminds me of recording a copy of a copy of an analog audio tape over and over. The image quality continues to degrade each time you save it. You can minimize that problem by using the lowest file compression possible when saving your JPEG pictures. Or you can avoid the problem entirely -- if you have enough storage to handle larger files.

TIFF: better, but bigger

If you're looking for a file format that doesn't automatically throw away a little bit of quality every time you save it, then you might want to try TIFF. TIFF files are larger, and your camera saves them more slowly. The upside, of course, is that the TIFF format is absolutely lossless. Some people compromise in this way: They shoot in JPEG, edit their photos on a computer, and then save the files in TIFF. Sure, they've lost some image quality up front, but any additional changes they make to the file will be lossless because it is now a TIFF.
My opinion, though, is that the TIFF format is generally more trouble than it's worth. The files are big; working with them is slow; and you can't e-mail the files efficiently, nor can you upload them to the Internet.

RAW: for the tinkerer

That brings us to the RAW file format.
A few years ago, I would have said that RAW was even more trouble than TIFF -- and, in a way, it still is. If your digital camera supports RAW (not all do), then when you select that format it saves your photo before any white balance, sharpening, or other effects are applied. You get an unprocessed source file that is untainted by any kind of filters or processing.
If you like to tinker with your digital photos, that probably sounds great. And it is: RAW does not discard any information, so it saves even more color information then either JPEG or TIFF. That's one of its pluses. Here's another: In the last year or so, almost every major photo editing program has added support for the RAW format, so it's far easier to work with than it used to be.
But the disadvantage of RAW is that you pretty much have to tweak all of your photos on a PC, adjusting their white balance, sharpening, and other characteristics. And when you're all done, you'll need to save the picture in a different format, such as TIFF or JPEG in order to e-mail, share, or post to the Web. Bottom line? You have to really take your digital photos seriously to have much interest in RAW.
For more on the format see Shooting in RAW