I've done a bit of work tonight digging around trying to make the YouTube BBCode a bit more user friendly and despite a few successes, overall, it was proving to be more complex than you'd believe to try and put all the various options into a single code.
So a bit of digging around and typically someone else has got there before me and I could have saved myself a couple of hours work had I just looked to start with

The old youtube, vimeo and dailymotion BBCodes will still work but are now hidden in the posting window in favour of the new video code.
This will play videos or playlists from Youtube, videos from vimeo, dailymotion and even ustream (but only recorded videos not live events from ustream). Works with http:// or https://
A few examples:
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To a Youtube playlist:
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[video]https://www.youtube.com/playlist?list=LLiMhD4jzUqG-IgPzUmmytRQ[/video]
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Or to one video within the Youtube playlist:
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[video]https://www.youtube.com/watch?v=caXNRdNaFVk&index=1&list=LLiMhD4jzUqG-IgPzUmmytRQ[/video]
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Or just to an ordinary video on Youtube:
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[video]https://www.youtube.com/watch?v=wYNfY9rEAG4[/video]
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Using the shortened youtu.be style share link from Youtube
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[video]http://youtu.be/fJ9rUzIMcZQ[/video]
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A video from Vimeo:
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[video]http://vimeo.com/13416084[/video]
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From Dailymotion:
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[video]http://www.dailymotion.com/video/x1qzjo9_queen-another-one-bites-the-dust-live-at-wembley_webcam[/video]
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From Ustream.tv:
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[video]http://www.ustream.tv/recorded/53944375[/video]
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So basically put to embed a video on here from Youtube, Vimeo, Dailymotion or Ustream or a playlist from Youtube just enclose the URL to it within the video bbcode (press the video button in a new post window and paste the URL inbetween the two parts.
Any issues or questions please let me know.