Well guys, it looks you are right. Although wordpress.COM is based on wordpress.ORG technology it seems that they have developed their own fork. Too bad, because the shortcodes from wordpress.COM are so elegant.
I now achieved what I wanted to and that was embedding a youtube video in a size I can specify myself. That is possible by using the old embed code from youtube. Goto the youtube video -> click share -> click embed -> click use old embed code -> copy, modify and insert the code into your page.
As mentioned by SelfHostedWP.com this job can also be done using plugins. I jsut tend to avoid installing plugins wherever possible.
Thanks guys
Aleks
But why?
The shortcodes are supposed to work out of the box: http://en.support.wordpress.com/shortcodes/
