Hot pixels aren't so bad. These bright spots come from electric leakage at the pixel level while the sensor is on—i.e. during an exposure. They're more prevalent at higher ISOs and with longer shutter speeds, because there's more opportunity for error and for those errors to be amplified. They're usually fairly well dealt with, thanks to in-camera processing designed specifically to handle them.
Stuck pixels are a little worse, as they appear in all exposures across every ISO. Unlike hot pixels, they aren't in any way subtle. They're 100% on, all the time, and they translate into bright white, red, green or blue pixel spots visible sometimes with the naked eye. These pixels aren't quite so random as a hot pixel can be, as they're always on all the time. They're a lot like dead pixels, but brighter. Dead pixels are a lot like their name implies: photo sites that aren't doing their job. They create black pixels in finished images. The good news being that camera software usually does a decent job of mapping and masking both stuck and dead pixels.
To test for hot or stuck pixels in your own images, crank up the ISO in your camera, put the lens cap on, and shoot an exposure that's nothing but black for, say, 30 seconds. Load the image into your favorite photo editor and, voila, any hot or stuck pixels will reveal themselves.
Defective pixels are usually removed automatically by a pixel map contained within the firmware of the DSLR you're using. If you figure every photo site has an X and Y coordinate, the camera can learn at which coordinates the pixels are bad and interpolate its way around any problems in the output. It's a pretty cool solution, and it's akin to the noise reduction that occurs in high-ISO digital captures.
If you've tested your camera and found a stuck pixel, the best way to reset it is to run the manual sensor cleaning procedure for a minute. This resets the pixel map in order to hide the stuck pixels from your pictures. Good as new.
There's one big caveat to this procedure, and it's becoming more and more of a predicament with the influx of HD video capture in DSLR cameras. Pixel mapping isn't active during video recording. That means a single stuck pixel—such as the one I found in a clip I recently shot—can become a big-time bummer. In order to repair my one stuck pixel, I'll need to send my camera in to the manufacturer for repair.
There are a couple of other options for those who don't want to ship off their cameras over a single little pixel. You can live with the problem—which can often be relatively easy since a single pixel is easy to miss—or you can repair the pixel in post. With still photography the pixel repair is simple; you can even make a batch process to take care of it automatically. But chances are you're not seeing stuck pixels in stills after you've done the sensor cleaning. It's the video that's got you down, and those procedures require one more step: software.
There's no one-click automatic solution for hiding stuck pixels in video, but there are a handful of downloadable video fixes that map and repair dead pixels in the computer. There's the Dead Pixel plug-in for Final Cut, Virtix's Pixel Fixer, and the DH_Reincarnation plug-in designed to bring dead pixels back to life.