This is the first quick animation style I thought I would look at. There is something about a GIF (Graphics Interchange Format) that I have loved for a long time now. As small and simple as they are (to make too), they can still portray the animation principles. To make a GIF all you need is photoshop and a small image sequence to work with. I suppose they are very similar to flip books, but they are just a digitalised form.
I had a long look through my Tumblr account (I used to be a bit of a blogger...) to find some of the best examples of GIFs that I like.
GIFs have also been made from small sections of Animated films or small animation shorts.
There is also a really good website with professionally done GIFs :http://www.gifparanoia.org/
Some are really well thought out, so it is well worth a look.