EXCELLENT digicam: Panasonic DMC-TZ1 I love mine!!
http://www.dpreview.com/reviews/specs/Panasonic/panasonic_dmctz1.asp?dontcount=1
Prioritize what you want in a camera. All-in-one digicams are lighter, smaller, and generally more user-friendly than most dSLR cameras, but tend to have far more noise issues, particularly in low light. (So far, I have NO complaints with mine, but your mileage may vary.) DSLRs can take exquisite shots that you can enlarge big enough for wallpaper (just about), but lenses may EACH cost more than an all-in-one digicam that would have been quite adequate. One tool that DP Review offers is a feature search... I highly recommend trying it, especially if you're not sure what class of camera you'd be interested in.
http://www.dpreview.com/reviews/compare.asp
Read as many professional and USER reviews as you can... but do keep in mind what style of camera you are looking at. It drives me nuts when users complain that an all-in-one digicam doesn't have the interchangeable lenses of a dSLR, for instance. Good luck, and let us know what sorts of things pique your interest!