Come on, LeonhartGR, recommending a hardware solution for recording PC? Don't get me wrong, the HD60 is a fine piece of tech and I want one myself, but it's not really good for recording PC unless you've got it connected to a second PC.
Typically I recommend OBS for free capture software, and Dxtory for paid software. OBS is more streaming-oriented, and much less versatile as far as codecs, compression, etc. if all you're doing is a straight capture, but it's definitely well worth the entry price of free. Dxtory provides less of a performance hit (in my experience it's the best out there for performance), but at the cost that it's more difficult to use, and utterly useless for streaming.
Some folks recommend FRAPS. It works, but I wouldn't pay for it myself; it's not enough better than OBS to be worth money, or Dxtory at all.