I had a tough time migrating from Blogger to WordPress and to add to it – I had to look all over the internet to find a FIX for this problem and finally, Jack provided with one, though he wouldn’t allow me to comment on his post and I lost the link!!
Here are the steps::
1) We need to turn-off Rich Text Editor for the respective user. For this, we need to click on (->)
->Users->Your Profile-> Uncheck the Check Box which says “Use the visual editor when writing”->Update Profile
2) Get the embed code for the video from Youtube or any other video upload provider.
3) Paste the code in the editor and I would recommend using “<div align="center">
<object width="425" height="350"><param name="movie" value="http://www.youtube.com/v/d589LnIGW9o"></param><param name="wmode" value="transparent"></param><embed src="http://www.youtube.com/v/d589LnIGW9o" type="application/x-shockwave-flash" wmode="transparent" width="425" height="350"></embed></object>
4) Repeat the above steps with the “Check Box which says “Use the visual editor when writing”” CHECKED in case you need to use the rich text editor. I am not using it for this post though!!