I ditched a regular video camera for a Casio Exilim EX FH-100. Over 10 megapixels, awesome features for getting around shutter lag for still pics, 1080 HD video, and very applicable 120 or 240 frames-per-second modes that are AWESOME for analysis in programs like Kinovea.
Running under $250 right now on Amazon, but you need to get a high volume, high quality memory card to go with it. The whole setup will cost you less than $300 and fit in your pocket. I probably am done with traditional video cameras after seeing the usable quality I got from this.
What memory card do you recommend? What capacity would I want? Not looking for anything extravagant. Maybe enough to hold ~60minutes of video.