A coworker was asking me about digital cameras today. He's looking to buy one as a gift and really wasn't sure what to look for. I sent him a link to a nice primer I found on Boston.com, Nine questions to ask when purchasing a digital camera.
If you're new to digital photography this article will give you a leg up before you hit the stores. It covers the main points well, megapixels, optical vs. digital zoom, batteries and storage media. As with most things today different users have different needs and the article is quick to point that out and give you a good basic foundation to build on.
Once you're ready to get started you should check out another great source, Steve's Digicams. This site does very comprehensive reviews of digital cameras with sample photos from each and "Steve's Conclusion" which cuts right to the chase. There's a ton of info on this site.
My wife and I happen to favor lens quality over megapixels and we prefer SD cards for storage to keep to a standard, plus they're pretty reasonable. We're not real big on teeny-weeny either. They just don't seem to fit right in the hand. For a small, carry around, I won't croak if I lose it kind of camera we have a Canon PowerShot A540 . It's small enough to tote but has a knurled edge that aids in one hand shooting. It's also got a lot of features and functionality for the price. There are newer models out in the PowerShot line, be sure to check them out.
Of course there's a lot of options out there and there's a camera that's right for you. Take your time and do your homework. Then get out there and start snapping!