You Tube videos are also all encoded H264 and are starting to be converted to HTML5 so they should run OK on Safari on your Touch. They run fine on my 3G iphone on both Safari and the You Tube app. When you enter the You Tube URL it should convert to the mobile version (m.youtube.com).
However there seems to be a problem with the 3.1.3 software release on the Touch and people are reporting the same problem as you. Go here
http://discussions.ap...y.jspa?categoryID=221 and type You Tube into the search to keep up to date with possible fixes