There are a number of packages available for both the mac and PC; unfortunately none are perfect in every way - so you have to weigh up your requirements
A lot of schools have turned to icananimate recently, mainly because the licensing is easier, but it also works well. There are some compromises in terms of functions and quality but this is an ideal package for young groups. No loop facility. Now available in a version for the iPhone and a pro version called proanimate which can loop, capture at very high quality (12mp apparently) and control a canon stills camera.
Hue have now designed animation software to go with their funky little web cameras. Our only bug with these cameras is that the auto exposure and auto white balance functioned terribly for animation, making your work flicker more than for any other camera. (this was early in 2010 so the problems might well have been ironed out)
Hoorah someone is making a FREE piece of animation software, it is a little basic, but very good.
Is a great piece of high quality software. They annoyingly have all sorts of different pro and semi pro versions which can confuse you, however, they are the only company who regularly improve their software.
The first low cost animation system available on any domestic computer; still pretty good even if no-one seems to be updating it, beating some of the others for basic requirements and quality. This is a little slower because it records every frame as a unique uncompressed picture, however, the plus side is you never lose a single frame.
Many packages have 'stop motion' in their title - don't let this mislead you, you can & should use them for drawn, cutout & pixilated projects too
Is probably the best bet on the pc, it comes in a basic version and an advanced version. The basic version is fine for almost everything you are ever going to need.
This is now available on the PC and we are hearing good stable reports so far
Is a basic animation tool for the pc, its free and if you can get past the 'difficult-to-read' website it's a good tryout
Some software comes with an upsidedown feature which helps you work on cutout and drawn projects with a tripod or rostrum