I've been finding lots of paper models on the net today - firstly over at Flying Pig, who sell paper automata to make at home - some nice ones there - if you sign up for the newsletter there are even some freebies.
some others include maps of the world which you cut out of a sheet of paper and stick together
Here's a site with all manner of polyhedra to print out and make. You can make a paper steam Engine (might get soggy when you add water still it'll stop the fire from burning the paper!).
Some lovely kitsch stuff here. Loads of free stuff here
And look, since it's the Internet, there's even paper automata porn