What do you want to use the camcorder for?
Generally, I would be looking for things such as:
(1) Resolution - does the camcorder record standard definition (SD) or high definition (HD) - and if it's an HD camcorder, does it record in 720p (720 horizontal pixels - progressive scan) or 1080p (1080 horizontal pixels - progressive scan) - 1080p is "full HD" and will give you the best picture quality - although this is only really relevant if you have got a "full HD" television or a suitably high resolution screen to play the video back on. Some camcorders may record in 1080i as opposed to 1080p - this is "interlaced" rather than "progressive", so slightly less good in terms of picture quality compared with 1080p - but still good.
(2) Recording media - some camcorders record to memory cards (e.g. SDHC cards) - some record to built-in hard drives - some even record to mini DVD discs. As SDHC memory cards are pretty cheap these days, I'd probably be looking for a camcorder that recorded on those - I wouldn't really be so fussed about it having an internal hard drive personally.
(3) Recording format - as far as I know, AVCHD is probably the best format for recording high-definition video in terms of picture quality and recording time - it uses very efficient compression algorithms to store as much video as possible within a given amount of memory. Other camcorders record in MPEG - which isn't as efficient as AVCHD - so you won't be able to record for as long before your memory card fills up, compared with AVCHD. Then, a lot of digital cameras that have video recording functionality record in a format called "motion JPEG" - where they take a separate JPEG image for each frame of video - which eats memory for breakfast so is really only suitable for very short videos - say 10 minutes or less.
(4) Quality of optics - including the amount of optical zoom - optical zoom is where the lens of the camera moves to zoom in and out - as opposed to "digital zoom" - which is where the camera just uses a smaller proportion of the sensor as you progressively zoom in - with the result that the more you zoom in, the more blurry and pixellated the image will get. So go for the highest range of optical zoom that you can get, and don't be impressed by a huge digital zoom range.
(5) Ability to record in low light. The best camcorders will still record with reasonable quality in low light (e.g. in a room at night lit with standard electric light - or when out at night) - whereas poorer quality camcorder may well give you a fuzzy or noisy picture with very dull colours by comparison.
(6) Quality of the microphone. Ideally you want at least a camcorder with a stereo microphone. If you can get a camcorder with an input for an external microphone then all the better - as the quality of most microphones on consumer camcorders is usually a bit crappy - so if you have the option of plugging in a much higher quality microphone, then this could be a lot better if you are serious about recording video with decent sound.