I'm using windows 8 with Chrome and have no problems playing youtube within the forum I did have a problem a couple of days ago and solved it by doing the following.
Type about

lugins in the address bar
Find the plugin that says "Flash"
If there are 2 or more files installed then click the -detail tab on the far right of the page
Disable two of the plugins If you have one with the address C:\Users\NAME\AppData\Local\Google\Chrome\Application\21.0.1180.60\gcswf32.dll leave that one enable but disable the others
Close chrome and re-open.
This may work it's worth a try..
And yes it was only on this forum that I had the problem but doing the above did solve it, it seems that the plugins affect Chromes built in flash player on some sites....