You can change the speed of videos on YouTube if you are using the HTML 5 player rather than the Flash player. To check which version you are using you can visit the YouTube HTML Video Player page. There you can see whether you are using the HTML 5 player and switch to using it if you are not.

Once you have switched to the HTML 5 video player YouTube will no longer use the Flash Player to play your videos. By clicking on the gear at the bottom right of videos you will now be able to change playback speed.

Related links:

Enable Variable Speed Playback in YouTube (LifeHacker)