I am an amateur and currently use a digital camera. Fujifilm Finepix 2800 (2 years old, so there are newer versions on the market now). It has a 2M chip and 6x optical zoom. It only cost me around $400 and is a great and useful all-purpose digital camera. All of the digital pictures I have on my website are taken on that camera, and for me it's a question of anticipating the right moment during a dance to push the button.
Now the downside to this camera... it does not take good pictures in relatively dark settings (as dances tend to be) because the autofocus relies so much on a well-lit object. Newer digital cameras have a "red light" that they use to focus in dark settings, and if you plan on having your camera take shots at many dances or parties where lights are dim, you should really consider getting one of those cameras.
Now, I would not mind a more professional camera, with greater zoom, better response time, and faster recovery time after taking the picture. With a good attachment flash, it is pretty much what you want when it comes to taking action pictures. Granted, you will spend a lot more for those cameras, so it depends on what you want with your camera.
So important items in summary, if you are doing this specifically for dances, assuming a digital camera.
1) Optical zoom (the higher the optical zoom, the closer your shots; digital zoom is different than optical zoom).
2) Dim light feature
3) Good flash and good chip response to light
4) Disk capacity (you may have to buy a higher-capacity disk, so you can take 300 pictures like I can [128MB])
5) RECHARGEABLE BATTERIES (NiMH)... buy two sets of 4 and always keep them all charged up before you go to the show you want.
You also will note, some of the cameras have a "movie" feature (60-sec max). The movies you get won't be excellent HDTV quality, but they may suffice when it comes to seeing the action of various dancers. However, I will also say, please respect any requests not to take videos during shows. (I never take videos of pro couples doing showcases unless I get their express permission beforehand.)