Picture in picture for my face while recording video games
Xsplit is a popular software choice for people recording and/or streaming video games. It allows multiple inputs and can overlay video on top of video, as you'd need for the PiP effect. There is a small fee to purchase this, but would highly recommend it if you are serious about it.

Another popular solution is Open Broadcaster Software (OBS) which is similar to Xsplit, but is completely free. Here is a guide to using OBS. When you setup a "Streaming Profile," you can just set it to locally record.

With both services, you have the option to record footage locally (such as to edit/produce and then upload to YouTube) and/or stream directly to an online streaming service (such as Twitch or Ustream).