Apple has removed that features in Snow Leopard and QuickTime X has no preferences panel to enable this. So you need to go through the command line to get it back...
In Terminal, copy/paste:
defaults write com.apple.QuickTimePlayerX MGPlayMovieOnOpen 1
Now movies will autploay when you double click them.
Comments from long ago:
Comment from: Bredbånd
This actually worked for me, so thanks a lot for the info :)
Comment from: Isaiah
WOW. THANKS for the the post. I was looking for a solution to this for a long time. It works.