RAW vs JPEG
1. JPEG is an 8 bit format, RAW is between 12 and 14 (though it can be less, it really depends on a variety of factors). Either way, RAW has more information available. That extra information allows for processing control that is lost if the camera makes the JPEG decisions for you. You can, for example, often recover blown highlights or underexposed regions, to a point. It's not a panacea, but why lose that if you can avoid. A note for purists... You could do a lot of the same with film in the old days. Somebody with the right talent in a darkroom could often recover what mass-market machines could not.
2. RAW is more forgiving because all you're really doing is capturing the sensor data, not telling the camera how to interpret it. So, for example, I leave my camera on auto white balance because it doesn't matter if I save in RAW, the white balance isn't applied yet anyways and I'll set it in post processing. For JPEG, if you make a mistake on white balance, or leave it on auto, it's going to be much harder to fix and the fix, by the nature of JPEG, will be destructive to the image.
3. RAW offers "non-destructive" editing options. By that I mean that when you process the RAW image data, the processing options you make are not baked into the original, you can easily undo them well after the fact, and so it is safe to save the original with your processing choices. JPEG, it's baked in, so if you want to avoid lossy destruction of your original image, you have to save as a new file which is, by the nature of JPEG, going to lose additional information in the process. Successive saves of JPEG is a bit like copying from old VCR tapes, each copy gets worse.
4. RAW offers fine-grained control over the development choices. For example, with sharpening in Adobe Camera Raw, I have four control mechanisms on the sharpening that allow me substantially more precision than the camera options for JPEG development. Same as true for noise reduction, lens correction, and more. Net effect, it creates flexibility in your outcome that is lost with letting the camera do it.
5. Scaling a RAW image with higher bit depth is going to produce a better outcome than scaling a JPEG. JPEG has lost, already, bits of colour information and it has alredy discarded pixels in the compression process. Scale and you lose more.
6. Format conversion is more flexible in RAW. I can save to 16 bit TIFF and retain sensor data that cannot be saved if I go from JPEG to TIFF.
Now, all this wonderfulness of RAW isn't without some disadvantages:
1. File size. RAW files are substantially larger than JPEG and so you can fit less of them on a card and less of them on your harddrive. On the other hand, disk and storage media are amongst the cheapest things you'll buy in your photography hobby, so load up on them and forget about file size.
2. You have post-shooting work to do. You can't just take the RAW file off the camera and slap it up online, you have develop it. So, this is probably the biggest reason that people avoid RAW. However, I shoot a lot of pictures and only spend the time on what I intend to publish. As you get practiced with it, and become more familiar with your gear and the software, it becomes substantially easier. I'm not a pro, and if I spend more than a couple of minutes on an image, I start to evaluate whether it is good enough to post. Having said that, I like to play with processing effects such as cross-processing and saturation/colour balance to create interesting outcomes and so those images take a little longer.
Now, you don't have to jump into RAW shooting with both feet if you don't want to. Depending on the camera, you can sometimes choose to shoot both. Pentax offers this option on all their current dSLRs and, I think, Canon is starting to do this too. Basically, for Pentax shooters, there's a RAW button on the left side that, when pressed, will save both the RAW and the JPEG image. That lets you try processing yourself to see just how you stack up against the camera when it comes to it without risking a loss of an image because you're not sure what to do. Also, with Pentax, you can set it do this mode all the time. So, as I said, risk free.
This, by the way, is a much longer version of a response I made on Photographr.info a few days ago. You should visit the site, a very friendly place to ask photography questions.