I've tried applying a couple coats of Krylon Satin Finish spray, but it didn't seem to have much effect. (Good if you just want to preserve the finish and texture of your paper and protect it a bit from dust, though.) I've also tried clear nail polish, but it didn't create the coating I was looking for.
This was my latest experiment: Minwax Polycrylic, purchased at Home Depot. I got the semi-gloss after standing in the aisle paralyzed, trying to decide whether I wanted a glossy or satin finish. So I aimed for the middle.
I tested the stuff on these origami sakura blossoms I folded from 2" squares of plain computer paper. Get a tutorial for the flowers here! After glueing the petals together, I also glued the loose flaps down to make them extra secure.
The polycrylic built up a nice, shiny coating and dried crystal clear with no brush strokes at all. The flowers are slightly flexible, but really tough, as if they were laminated with clear plastic or packing tape. Mission accomplished!