Actually, i'll put the one thing that isn't a YouTube video first:
This thing is described as a game, but really it's just a app that will make music and display visual effects when you hit keys on the keyboard. I've certainly played with similar things in the past, but it's fun to mess around with for a bit.
Now for the videos:
The Game of Thrones Honest Trailer. This is the spoilery version, but right at the start they warn you and provide a link to a spoiler-free version that you can click on. Also warning, the last 30-60 or so are a compilation of pretty much all the nudity in the show, with small black bars covering nipples and the occasional groin shot, so if you're watching somewhere where that would be a problem, be prepared to stop it as soon as it gets to that part.
On a related but entirely different note, someone put together an 80s sitcom intro for Game of Thrones.
Here's a cute little animation about a ghost girl dancing with a pair of possessed shoes.
Here are two "unnecessary censorship" videos. On a rating from 1 to 10, where 1 is suckage and 10 is "The Count Censored", these are probably about a 6-7.
And to end on a somewhat inspirational note, here's a segment of a speech Neil Armstrong made talking about how awesome engineers are, set to animation by the guy who does PhD Comics.