Origami ATC's, in particular, have an origami model glued to them, or they are letter folds whose final size is 2 ½ x 3 ½ inch (64mm x 89 mm).
Every year, as part of the activities for their annual convention that takes place at the end of June, OrigamiUSA organizes an Origami ATC swap. I've been participating in the ATC swaps for three years now, and I really enjoy it. Here is a pick of the cards that I'll be trading this year:
The hearts on the cards are my design, and were folded with 3" (75 mm) squares of patterned kami paper.
You can find instructions to fold the hearts in here. There is also a video available in the Videos page.