I'm running Raspbian. I installed Gnash to enable Flash support (i.e. YouTube playback). The videos come up, but they're too slow to be watchable.
Does the MPEG-2 licence key improve YouTube playback using Gnash?
Unfortunately it won't. First of all, flash video does not support MPEG-2 for encoding. Secondly, in order to use RaspberryPi hardware decoding capabilities (and MPEG-2 licence is exactly for this decoding mechanism) you have to use RaspberryPi OpenMAX libraries. This means that only applications with specifically written to support RaspberryPi hardware decoding can benefit from it.
There is currently no good way to play YouTube video directly inside of web browser. You can, however, play this videos using hardware acceleration from external programs, giving them the URL. Here's an example of such program.