My current camera is a Canon Power Shot A700, I bought it in early 2006. I recommend it. A very nice small camera (6 megapixel, 6x optical zoom). The best thing about it though is the 2Gb memory card - I can go an a vacation and take the highest quality photos and they all fit on the card. That was the largest one available at the time. If there is a larger one I would get that now (and in fact I probably will before my next trip, I came close to filling it up and the flash cards are amazingly cheap now). Canon offers great service too.
Here are some photos from a trip to Boston taken with the Canon A700.
Previously, I bought a Fuji FinePix 3800 in June 2003 and which worked for a couple years and then died. I didn't want to buy another Fuji. I bought, and recommend, the 256 MB xD card (the camera comes with a 16MB card). It holds a remarkable number of photos - hundreds at the 2MB (1600*1200) and nearly a thousand at the 1 MB level (the quality at the 1MB level is great for viewing on a computer - printing larger than 5*7 photos would be better at higher levels).The only problems I have had so far are: