Recently, I have been fielding a lot of question on which cameras are good for taking videos.
Generally speaking, I strongly suggest going with an HD video recorder simply because standard definition models have seen exactly zero technical development for quite some time now. Models still on the market are simply legacy units.
I am more of a still photo kind of a guy, but I do take a lot of videos in an attempt to record some of our family stories and some of my table tennis and martial arts practices. My recommendations here will be mostly aimed at people like me, who need to take some videos, but do not want to spend any more time than absolutely necessary on editing, converting and otherwise messing with the clips.
I do not think most people need a standalone camcorder. There has been a lot of convergence between camcorders and digital still cameras in the recent years and I think you will be better served with a decent DSC (Digital Still Camera) that has a good video mode. That will give you a chance to carry one (hopefully compact) gadget with you for both snapping pictures and taking video.
As far as the video resolution goes, 720p is sufficient, but 1080p is better. However, I would not base the decision based on the difference between the two HD modes (besides, even with a 1080p capable camera you might choose to use 720p mode for the most part).
One key difference between DSC cameras and camcorders is that DSC cameras are typically equipped with much wider angle lenses which comes in handy for sports recording when you need to have the camera fairly close in, but still need to look at a large area.
Then there is the recording format to consider. I strongly suggest you go with H.264 (MPEG-4) compression in a MOV or similar file format. The trendy AVCHD compression that is based on H.264 is much harder to work with, so unless you plan to do some serious videography, stay away from it.
Another option is the older Motion JPEG codec, which gives you good quality, but much larger file sizes.
Now for some specific recommendations.
Canon SD4000IS is a very nice option in a startlingly small package. Both still image and video quality are pretty decent and it gives you a pretty cool slow motion video option. 720P videos are recorded in MOV files which are easy to play with Apple’s free Quicktime player (and easy to edit with the very inexpensive and easy to use Quicktime Pro):
Keep in mind that Canon just announced an updated version of this camera (SD4500IS), that will record 1080P video clips, so SD4000IS is likely to be well-priced. For my purposes, I actually prefer the SD4000IS, since it has better wide angle and brighter lens. SD4500IS does give you a lot more telephoto and a nicer LCD:
I would also like to repeat the recommendation of Casio FH100. While video recording is in larger size Motion JPEG mode, the quality is decent and lens range is more versatile. A couple of people bought this camera upon my recommendation and they are very satisfied with it:
FH100 is a bit bigger than the Canon SD4000IS, but offers much longer battery life, and more flexible lens (both wider angle and more telephoto). On the other hand, the SD4000IS has a much brighter lens, so low light performance is likely to be appreciably better.
Lastly, if you care about sound quality more than video (which is the case with some family stories I try to record), Zoom Q3 is worth a look. I have a standard definition version (HD has just been announced, but not available yet), and while video quality is somewhat mediocre, sound quality is very good.
I hope this helps.