The Casio Exilim EX-Z750 is a fantastic camera with a tricky name. It features a number of things that make it still, after a couple of years, the best in its class. Plus, you can pick it up pretty cheap online nowadays.
The thing I like best about the camera is that the movie mode is amazing. It uses the mpeg-4 codec to deliver a very high quality movie mode. This isn't some camera phone looking video, this is nearly camcorder quality.
The pictures, the most important part, are also astounding. It has a great color balance, minimal purple fringing and crisp pictures in low light. The only thing that it doesn't to particularly well is flash, because it's weak and will make the people you shoot look like vampires.
Overall, a great camera at (now) a great price.