Personally I use Fraps to record games with a high FPS and then Camtasia to record games where there's not much fast paced FPS stuff going on and any desktop stuff. At the moment Camtasia is my most used as I've been playing a lot of indie games with small desktop displays
Search around the internet and download a few that you like the look of. It won't be an easy job..
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I use Bandicam. It gives you ten minutes with the free edition, plus you can target a small area on the screen for filming, making it handy for flash game filming.
Depends on your specs. If you have a lot of HDD and a very decent PC, go with Fraps. if not, Bandicam is a really good alternative and it's what I'm using right now.