I'll throw in another vote for the Canon PowerShot A620.
It's been a good camera for me since I purchased it in February 2006.
It's packed with features.
I bought a huge 1gig memory card and it's virtually impossible to fill up -- but more importantly it allows you to take full advantage of the video features (yes you can take digital movies with sound). I plan on using it to film a deer hunt this year.
One of the other great features of this camera is the AV cables that allow you to plug the camera into a television, and view your photos just as you would on the camera's LCD. Great for showing a few people some photos, rather than everyone trying to crowd around the camera.
The LCD window swings out and swivels in all sorts of directions allowing you to take pictures from difficult angles while ensuring your subject remains in the middle of your picture.
There's a color-swap feature where you can train the camera to make anything red, look blue (for example). It sounds silly but it's a fun feature. I think I'll take some pictures of a blue deer this year... that outta make people do a double-take.
Too many features to get into here, but those are just a few, and definitely not the more technical of the features available.
Here are a few pictures and keep in mind I know nothing about lighting, focus, or any other darn thing other than how to use a few of the camera's feature to my novice advantage: