I have a Canon Powershot A80 (4.0 MP) and also a Canon EOS 30D DSLR (8.2 MP) The 30D was a b-day gift for Erin, but we're a team, so ya know, it's basically mine...haha.
The primary advantage of an SLR is interchangeable lenses (so you can buy REALLY nice, REALLY expensive lenses) and also the single lens reflex-- What you see thru the optical viewfinder is coming in thru the lens itself and not a little parascope out the top. This allows you to avoid parallax at close range that is a problem with Point and Shoots.
That said, you can take awesome photos with a Point and Shoot. My little A80 has complete manual control should I want it, and I use it all the time to adjust my exposures. The shutter lag is not really noticeable, because I use the "hold-the-button-halfway-down" technqiue. When you depress the shutter release halfway, it activates the auto-focus, and you can aim that sucker at anything and it actively focuses(you can hear it...chttt...chzztttt...robot sounds.) Click the rest of the way and your shot is instantly taken, no delay.
I've shot with both the A80 and the 30D, and I take a lot of action photos...skiing, mountain biking, etc. There is no good reason to strap your $1500 DSLR to the strut when you can send your $299 Point and Shoot out to do the job and get nearly the same quality. You can get wired and wireless remotes nowadays for the little cameras too. You can even buy wide angle conversion kits for the little Canons.
Jr is correct about the pixel density issue. Lower pixel density = less noise in the photo. The 8.2 MP 30D is a higher level more expensive camera body than the 10.1 MP EOS Rebel XTi. One thing I guess we can take from that is that megapixels are a poor metric for evaluating a camera. Most people use that as their sole comparison between cameras, and it's hardly relevant over 6.0 MP, and for the noise issue.
Unless you're a serious photographer and want to spend more money on lenses (the lenses that come with the DLSRs are not that great) you're better off with a Point and Shoot. Here's a sample of a shot I took the other night with my A80 up on Rattlesnake Mountain here in Reno:
Here's a similar photo taken from the 30D:
Like Mike says below, it depends a lot on your objectives. High resolution and quality glass are key for print, but for web you can get away with less. This is a
great site for camera reviews. They take sample shots at various ISO settings so you can see the quality degredation with emulated "film speed."