I tried pretty much every 2.5 extension and spent a good amount on a number of them. However, I couldn't find anything that met all my requirements until I tried Youtube Gallery.
Quite simply it is the best available. Installation was a breeze. You add categories and then video links into those categories. Next you design a theme that you then specify in the module - a much neater way of doing things and something that other extensions should follow the idea of.
Worked right away and after selecting the HMTL 5 player it also works on iPad.
Also, a massive plus is that it automatically generates the thumbnail for each video, something that most seem to forget. I don't want to spend time uploading individual thumbs so this is perfect.
The extension has tons of options to get your player and gallery the way you want it.
The only improvement I would make is for the backend to automatically show the original titles from the videos. You could then edit these rather than adding your own from scratch. It does drag in the original titles in the frontend but you have no way of knowing what the video is at the backend without playing it first.
That is a small gripe in what is an excellent product and well worth paying the extra small amount for getting the pro version.