Examples of origami used in science and engineering:

Ultra-cheap micromotor technology, allows cellphone cameras to zoom and focus. Folding makes a thin sheet of a piezoelectric ceramic material work like a motor.

The micro-origami technique used to fabricate directional-sensing photodetectors and corner cube mirrors provided with electrostatic actuation

A folding segmented telescope lens (Eyeglass) and another article on Eyeglass

Folding Deployable Membranes designed from folding Tree Leaves (pdf)
Wrapping Fold Pattern for Deployable Membranes
Deployable Structures

Tom Hull's site has a series of abstracts on the subject of the mathematics of Origami from the 3rd International Meeting of Origami Science, Math, and Education which include items like The Energetics of Crumpling, Origami Numbers, and Circular Origami: a Survey of Recent Results

An example of Tom Hull's origami art is in my "Museum of my Favorite Artists"

Computational Origami, the geometry of paper folding, an interview in New Scientist with Eric Demaine.

Bio-Origami: Protein Folding

Origami and Math by Eric Anderson

An article on David Huffman's origami work is here