I have a Nikon CoolPix 3100 with 3.1 MegaPixels. (Lithium-ion rechargeable battery or 2 AA -can be rechargeable- batteries)
Great for the type of amateur point-and-shoot stuff I do.
Basically I use that camera for making pictures that go onto my customers' websites.
The flash on it is a bit weak, but with a spot or 2 extra, the quality of the photos is great.
Extremely compact and light, it has a raft of scene modes to choose from, as well as automatic mode. It uses the cheap CompactFlash memory cards.
The newer 3200 is pict-bridge compatible (mine is not) meaning you can connect the camera to a pict-bridge printer and print photos straight off the camera (but you are waisting the camera's battery power).
Why anyone wants to do that is a mystery to me. Most pictures you want to look at first (e.g. on a PC), maybe make some corrections and only then do you print.
So all you need is a USB2 cardreader for your camera's card.
In the same Nikon modelrange, currently the CoolPix 5200 is topdog. (Lithium-ion rechargeable battery)
If you want wide-angle, look at the Olympus Camedia C-5060 (5PM), expensive though. (Lithium-ion rechargeable battery)
If I had to start again today, I would opt for the Canon Powershot A85 (4MP), I think this is the ideal first digital camera. Runs off 4 AA batteries.
Most important is not the amount of megapixels (3MP is more than enough for everyday shooting), but the size of the sensor. Look for 1/1.8 inch. This is a larger sensor than e.g. 1/2.5 inch (remember they are fractions of an inch).
Also important are fast startup time and small shutter lag.
Look for optical zoom rather than digital zoom.