YouTube: Get alternate video thumbnail still images, or larger sizes, from a YouTube video

YouTube stores 4 different images for each video that it has on file in it's monstrous database, with 3 different images for the default image.

And each song in the database has it's own unique identification key.
You can find the ID key in the video's URL or embed code.

For example: "We Found Love" by Rhianna and Calvin Harris is located at:
http://www.youtube.com/watch?v=tg00YEETFzg

So, the ID key is:
tg00YEETFzg

The thumbnail images that YouTube saves are called:
default.jpg
mqdefault.jpg
hqdefault.jpg
1.jpg
2.jpg
3.jpg

The image server is here:
http://i1.ytimg.com/vi/

So, you construct the image URL by putting the pieces together like this:
http://i1.ytimg.com/vi/tg00YEETFzg/default.jpg

So, you'd get your choice of these images: