I'd suggest Bandicam - it performs just as well as fraps, at least in my opinion. (That's to say - if you can't see any frameskipping as you're recording the video, you won't have a shock when you watch the recording back), and its free trial is much more reasonable.
The fraps free trial watermarks the recording and limits you to 30 seconds, whereas the bandicam free trial is more like 10 minutes (which is fine for most tutorials and Minecraft videos, for instance). It does still put a watermark in the centre of the video, at the top, but you can easily cover this up with a logo or username, or subscribe button when you're editing (or even an annotation, after you've uploaded). I don't think it's illegal to cover the watermark, or anything like that - it's just intended as an inconvenience to make you buy the full version.
After you've got used to the free trial, you'll probably want to buy the full version, and I don't think it's very expensive, at least compared to some things...
I've successfully recorded some Minecraft videos with the full version of Bandicam, which my brother bought recently.