Almost all new cameras will be able to print decent 8x10 prints —anything with at least 3 megapixels. You'll be able to transfer photos to a PC or Mac with a USB port, and many can now print directly to certain inkjet printers. Most cameras these days come with special rechargable battery packs. You can also take the memory cards to Walgreens and get 4x6 (a steal at $.29 each), 5x7 or 8x10 prints from their 1-hour photo printing system.
I particularly recommend not getting stuck too much on how many megapixels a camera has, if you don't plan to make prints larger than 8x10. Choose a camera with other features you like, such as size or flexibility in shooting modes.
Many digital cameras (but not SLRs) have "movie" modes, but I have yet to see one that produces movies of acceptable quality (24 or 30FPS at TV quality), and the built-in microphone is invariably terrible. Some cameras can't even change the exposure or zoom within a single movie, some are limited to anywhere from 30 seconds to a few minutes per movie, etc. Don't get rid of your camcorder yet.
Like film, digital cameras have an ISO speed rating. Unlike film cameras, you choose a different ISO rating for each shot, not just when loading a roll of film. As with film, a higher ISO rating enables quicker shutter speeds but adds noise (grain) to the image. SLR-style cameras typically go from ISO100 to ISO1600 or ISO3200, with images up to ISO800 showing fairly little noise. Non-SLR cameras generally have an upper range of ISO400, with images up to ISO200 showing fairly little noise.
Beyond what comes in the camera box, you may want to get
(3x) on a traditional 35mm film camera. Update, 2006/2/10: For Christmas, I gave an SD400 as a gift. I haven't seen any prints from it, but onscreen the pictures are detailed and colorful.
Nikon also has some good SLR offerings, the D50, D70 and D70s. I know less about them. However, people are angry at Nikon right now, and for good reason. They reportedly encrypt the photos their cameras take when they are in the highest quality mode, and won't promise not to sue software developers using the US law called the DMCA just for writing software that can work with the files from Nikon's cameras.
With these digtial SLRs you can use any lens that would work with their current film SLR cameras, but the size of the sensor inside the camera is smaller a than 35mm film by about a factor of 1.6. This is called the "crop factor". So a lens marked "18-50mm" will give you a field of view equivalent to about 30mm to 85mm on a 35mm negative.
Some photos my friend has taken with his S1 are here:
http://www.abstract.a3.photoshare.co.nz/
He resizes all the images before putting them on the website. The
actual photos are more detailed than this.
Some photos I've taken with the Digital Rebel are here:
http://photos.unpy.net/187339/
Digital Photography Review is a great site with in-depth reviews of many
digital cameras, though mostly it is about more expensive cameras.
Here are their reviews of some of the cameras I've mentioned:
http://www.dpreview.com/reviews/canonsd500/
http://www.dpreview.com/reviews/canonsd300/
http://www.dpreview.com/news/0402/04020906canon3ucs.asp
http://www.dpreview.com/reviews/canons1is/
http://www.dpreview.com/news/0504/05042201canons2is.asp
http://www.dpreview.com/reviews/canoneos10d/
http://www.dpreview.com/reviews/canoneos20d/
http://www.dpreview.com/reviews/canoneos300d/
http://www.dpreview.com/reviews/canoneos350d/
http://www.dpreview.com/articles/nikond50/
http://www.dpreview.com/reviews/nikond70/
http://www.dpreview.com/news/0504/05042003nikond70s.asp