FFG and others (Team Covenant for one) put up some great tutorial videos for the Star Wars LCG and the X-Wing Miniatures game.

Are there any video tutorials for the Edge of the Empire RPG?

Would be awesome to see a game being ran.

I have been searching YouTube and the internet for gameplay or tutorial videos, and I haven't found any.

No real videos that I know of.  But the order 66 podcast has a 2 part live skype game that you can download and listen to.  It's great help in getting an idea of howthe system works.  You can download any of the podcast for the EOTE system at http://feeds.feedburner.com/Order66

The celebrity live game is what you want.  Give them a listen, I think you'll find what you're after.  GM Chris does a great job running the game!  It's a lotof fun to listen to.

GM Chris did a much earlier live-play demo of EotE on JustinTV, with local players instead of it being recorded on Skype.  I took a look at the D20 Radio Channel, but it seems said live-play demo didn't get recorded.

Heh, my first post in the forums and I am going to sound like an advertiser, but this past Thursday the 17th of January the Thursday Knights webcast group played the first of at least two sessions from the Beginner boxed set.  This episode features the normal learning to play the game as they played the game and they were their usual entertaining selves.

They broadcast on TwitchTV and will be playing again this coming Thursday as well.  To skip the pre-game chatter pop over to 37 minutes into the latest video and also get to witness a perfect Star Wars RPG introduction.  Obviously there are spoilers for the Beginner adventure and there are a few curse words here and there.  For myself I found the episode both educational and  encouraging with respect of EotE.

Back during the beta the Order 66 podcast had a really nice example of gameplay. I can not remember what episode it was in though. Anyway it managed to make a battle with Mynocks have tension and excitement. FFG has developed a really great system and I would not mind them putting up some gameplay example videos on the site, help my players wrap their heads around it.