If you want to record high res (1280x720 or more) video of the games you play on your PC, you'll probably want at least a quad core i5 at around 3 GHz, or a dedicated video encoding card, whatever those are called. You'll also want a fast and big hard disk, because fraps videos have very little compression done to them during capture. For example, 20 seconds of 1920x1080 30 fps video takes 900 MB before post-capture compression. You can compress this later, of course, but while it's being recorded, it'll be this big.
Alternatively, if using fraps, you can make fraps record using fewer frames than the game runs at, as well as halving the resolution during capture. This will make videos a lot smaller.
If you want to record console games, you'll either have to emulate it (if it's a Wii/PS2 game or from an older console than those), or get a video capture card that has the inputs that your game system supports.
-edit-
I also just did a test for my ps2 emulator. Persona 4 runs at full speed while capturing 800x600 at 30fps, that's on a 3.2GHz core 2 quad. 22 seconds took 400 MB.
The lower the resolution, the easier will it also be for your PC to encode the videos with powerful compression in real time. If you want to stream things in real time on like twitch.tv, you should probably settle with a vertical resolution of less than 480, just to ensure that you can upload it in real time.