Most people think of little animals or figures when the hear the word, but I like geometric pieces. Most of the pieces I fold require 12, 24, or 36 pieces of paper. My favorites are the interlocking boxes.
I can make dinosaurs....that's about it, LOL. I've always wanted to make some cranes. I have a book from Japan on origami, and some paper from there too. Of course, it's written in japanese...but....step-by-step pics are worth a thousand symbols
I should really get my stuff out and try some more things.
I go in and out of folding periods. Got a few dozen books, most too advanced for me.
I've been stuck on a dragon by David Brill for a few years now.
I've done some boxes, fitting them together at the end is very cool.