There is quite the substantial list of recording/editing software out there and I can’t honestly say one will be better than the other. I can only say a few little things about the ones I’ve had experience with:
Fraps – The video quality is spectacular and this software has been around for quite some time doing updates and so on. The problem, though, is that these high quality videos are extremely large files. For a five minute recording, you’re looking at more than a gig.
Camtasia – I prefer this over Fraps because of its ease of use from both ends, recording and editing. The draw back is that it will not record full screen games, only windowed mode games. If the game you want to record does not have the option of moving to windowed mode then you’re just out of luck.
Free applications – I’ve yet to find a free recording software that doesn’t tell you immediately upon using that it’s free for a reason–it’s just plain terrible or it has only one functionality that can only be applied to one type of video. For example, CamStudio is a free software that records with absolutely terrible frame rates unless you set it to only record a certain pixel area around your mouse pointer. This would be something very useful to make a tutorial on how to click a button. You know, the technologically illiterate tutorials.
There’s no way I could give you a complete list of potential programs for you to use. Leave comments of other programs I haven’t mentioned that you have found useful!