In WordPress 3.3, there is feature auto embed for video site such as YouTube and Vimeo. If you have try and can't do it, there's several way you can do.
1. Go to Setting >Media at Dashboard and check the option auto embed.
2. If still don't work, usually it's because WordPress automaticly convert the pasted word start with http:// into clickable link. So you must remove the link into plain text.
If you need further customization such as the size, centering, you can use shortcode. visit HERE for more information.
Hope this simple tips helps.
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