The following pieces of animation are amazing. They are the kind of animation that I like. I want to do this kind of animation.
"Story from North America" (2007) by Garrett Davis and Kirsten Lepore.
Music written and performed by Garrett Davis
Lilli Carré's entire body of work
Beginning with this adorable music video
This trailer for an upcoming feature by Chris Sullivan, whose other work is also brilliant.
This tutorial by a young Terry Gilliam on how to do cutout animation.
I will also plug the work of Storycorps, which has only in the last few years started doing animation.
In conclusion, enjoy this beautiful animation stuff.