I'd like to correct a couple of misconceptions about RAW & JPG capabilities. I'm an electrical engineer who designs digital cameras, and I've also written JPG compression algorithms. The following information applies to standard JPG (& not jpg2000 which is not available in the majority of cameras anyway).
As others have correctly said, RAW keeps all of the raw pixel information, whereas JPG throws some of that information away. It's the WHAT that gets thrown away in JPG that's of great importance for underwater white balance.
First off, it's important to understand that at depth, red photons are *reduced* by the water column, but they're not removed entirely. There *are* red photons; it's just that there are a lot fewer of them at depth, which is why JPG photos appear blue. For that matter, non-white-balanced RAW images look blue too.
If you look at a RAW image taken under water, there is information (non-zero values) in the red pixels; it's just that they're a great deal fainter (dimmer, lesser intensity, whatever word you prefer) than if that same photo was taken above water.
So, with that understanding, let's now consider JPG encoding that image. You can think of JPG as being a 2-stage process. The first stage is to break the image into a luminance (brightness) field and a chrominance (colour) field. The luminance is like "black & white", whereas the chrominance is colour information. Typically the luminance field is kept as-is, whereas the chrominance field is reduced by 2, ie, every second line is thrown away. In this way we keep our full image resolution (in black & white thanks to the luminance field) and we keep a good estimation of our colour information (thanks to the now cut down chrominance field) while reducing our data size.
This works because our eyes are more sensitive to brightness (luminance) than colour (chrominance). So we can throw away some colour information without our eyes really noticing it.
Of course, we've just tossed away half of our colour information, and in the case of red we don't have much to begin with! This is not necessarily a great idea if we want to white balance an underwater photo later.
That was JPG stage 1. At the end of stage 1 half of the colour information has been tossed. Now we do stage 2.
In stage 2, for each of the two fields (luminance & chrominance) we perform a frequency analysis, where essentially "small things" are thrown away. When it comes to the chrominance field, this is where a lot of the remaining red gets discarded, because it's low intensity to begin with, and thus not very noticeable in the (mainly blue) image.
The end result of all this, as you can probably see, is that for underwater images we start with a greatly reduced amount of red-colour information, and then the JPG compression process naturally throws most of what little there is away. The end result is blue JPG images. But more importantly, they are blue JPG images with precious little red data in them, so post-processing the JPG image (in picasa or photoshop or whatever) to colour-balance it works fairly poorly. We've seen that in the example images earlier in this thread, where the JPG barracuda & shrimp images were white-balanced, but much less successfully than the RAW images were.
The simple fact is, to get a good white balance, you need information in all three colour channels (red, green & blue). Underwater we naturally have a shortage of red, and then JPG throws away most of what little red we do get. Not a great combination.
If you're going to insist on shooting only JPG images underwater, it's critical you do manual white-balances underwater (by balancing against the sand, or a white slate, or something). In that way you're telling the camera "bump up all my red values before doing the JPG compression". If you don't, and shoot a bunch of blue images, you'll never be able to white-balance the resulting JPGs later on in photoshop with remotely the same degree of accuracy as if you'd simply shot the image in RAW to begin with.
Changing gears slightly, others have correctly pointed out that shooting RAW allows you to pull detail out of shadows that cannot be done from JPG. That is correct, and is due to the 8-bit quantisation that's performed within the JPG algorithm. It's that same reason that gives RAW the ability to correct minor over or under exposures where JPG cannot.
I'm not going to tell the OP he should or should not be shooting in JPG; it's an individual choice. I can tell you that on land I shoot JPG. But underwater I shoot RAW. With 4 GB SD cards costing just a few dollars; with free programs like picasa supporting RAW; with not having to bother messing around doing white balances underwater; it's plain & simple both easier & better.
I hope this helps.