It is a bit time intensive but I do it like this.
Video Recording and Editing:Dxtory for recording the video and the game sound (thanks to Arka for the suggestion).
TMPGEnc Video Mastering Works 5 for editing and rendering the video.
Audio Recoding and Editing:Audactiy for recording my microphone and editing the audiotrack.
Audacity is freeware by the way.
I set my recording software up so it will not record my microphone and only the game (and teamspeak etc.) sounds. Before I start the video recording, I start to record my microphone in Audacity. A small trick that I have learned is this.
1. I open Audacity and start to record my microphone.
2. I go back into the game and press my keys to start the recording "a bit louder as it should be" so I know in the audiotrack where the recording starts and ends. In Audacity it looks like this.

3. When Im down recording, I also stop the recording in audacity.
4. I delete the audio before and after the start and end of the recording and I replace the loud button pressing with silence in the adiodtrack. By doing this the lenght of the video and the audio track are matching and everything is in sync.
5. After that I also edit out static noise or other unwanted noise from the audio track.
6. I export the audiotrack as a mp3.
After that I simply but the audio and the video in TMPGEnc Video Mastering Works 5 together.