There's a simple Greasemonkey script that forces YouTube to use the HTML5 player for almost all the videos you watch at youtube.com. You need to install Greasemonkey if you use Firefox or Tampermonkey if you use Chrome, then click the "Install" button here.
[Update (Octomber 3rd, 2013): For Chrome, use the old version from Sept 23.]
The script works better in Firefox. If you install the script in Chrome, it will disable the new Ajax interface, but everything else seems to work well.
Here's a video you can use to test the script. Please note that the script doesn't work for embedded videos.