Always play youtube videos in highest available quality, embedded ones too, on any site.
You can change the default quality level from highest available quality to lower qualities, eg. 720p, 480p, etc. On how to do that, see the SETTINGS part in the script.

Tested with:
Firefox 24.0 with Greasemonkey 1.12
Chrome 30.0 with Tampermonkey 3.5

GNU GPL v3