The issue is that this URL format
http://www.youtube.com/watch?v=PzBk4-awY40
...won't work with iframe mode (you are setting fancybox.iframe class in your link).
You may rather use youtube's embedded format, which works on devices that don't support flash
http://www.youtube.com/embed/PzBk4-awY40
Additionally, you can add the ?autoplay=1 trailing parameter if you want your videos to start right after fancybox is opened
JSFIDDLE
NOTES:
/watch?v= URL format (the links are set by the user or dynamically) then remove the class fancybox.iframe from your link and use the fancybox media helper instead. Check http://fancyapps.com/fancybox/#examples ==> extended functionality for more.false, check https://stackoverflow.com/a/16595607/1055987 for more