Rice cakes contain only rice and salt, so what holds them together?

Rice cakes have only two critical ingredients—rice and water. The rice itself needs certain characteristics to produce the best quality cake and limit breakage. Sticky rice, whether white or brown, tends to work best, while long-grain varieties don't expand during cooking as vigorously. Water is important early in preparation. Other ingredients like salt (added before popping or sprayed on after) and various flavorings are important considerations to taste-and nutrition-conscious consumers but are not significant to the production process.

The simple process of making rice cakes is based on the fact that rice subjected to the right combination of heat and pressure will expand to fill a given space. The manufacturer's specifically preferred type of raw rice (depending on stickiness, expansion potential, and taste) is soaked in water until the right moisture level is attained.

Read more at:

http://www.madehow.com/Volume-4/Rice-Cake.html

For another sticky thing to do with rice, see http://www.wikihow.com/Make-Rice-Glue (The linked page contains the statement "this recipe can be stored in a jar in the fridge" - Baloo thinks the rice glue would better be put in the jar, and the recipe kept outside the fridge.)