Yes, this is the oldest and apparently most frequently-broached topic here. :)
I believe what the solution is for making the YouTube embed code work. Apparently, it seems that you should not use the WYSIWYG editor (or instead, you should install an extra plugin)...
BUT.. this is a real big inconvenience when you actually want to use both the WYSIWYG editor. And I don't think that using the code-editor itself is a real solution. I hate hitting "save and continue editing" and then seeing that the YouTube video disappeared because somehow the "embed" tag turned into an "ibed" tag.
Is there ANY way to not have this happen? I noticed it in 2.0.x and I was hoping it was fixed in 2.1.x but... I'm sadly not finding a suitable solution.