Why do gliders have bungee cords in the control systems and what do they do? Are they on all control surfaces? What about ultralights?
The bungee is just a bidirectional spring that tends to hold the elevator at position x, and if you move the stick you are stretching the spring in one direction or the other.   They are used in the elevator control circuit to provide an adjustable centering force for trim purposes, and on gliders with all flying tails, a measure of stick free static stability (you don't get a lot - many gliders are mildly divergent in pitch if you aren't holding the stick, but this isn't a big deal since you are almost never flying hands off).  The glider's pitch trim control adjusts the "at rest" or relaxed position of the spring so it will tend to fix the elevator at this position or that unless overcome by a control input.

Normally you would have a trim tab on an elevator/stabilizer tail or a trim/anti-servo tab on an all flying tail, as regular airplanes do to provide speed-seeking trim and strong stick-free stability, but gliders operate with much lower loading and forces on the tail and can get away with a bungee spring that acts like a little man under the floor pushing on the stick, this way or that to try to hold it at a given position, so you don't have to.  This does away with all the linkage, tab surface etc, which is a big deal when you are shooting for a 40:1 or more L/D.

You can put bungees in any control circuit if you want to be able to trim it with an adjustable centering force, or want to increase the forces.  Some light aircraft use bungee springs in the rudder control circuit to provide rudder trim.  The spring just replaces your foot by exerting a spring force so you don't have to.  The downside is the spring loads are present when you move the controls out of the trimmed position, adding to the perceived rudder forces when maneuvering. 

I'm pretty sure there are ultralights out there that use elevator bungees for trim purposes instead of a tab.  However, driving the surface directly aerodynamically using a tab on the surface provides a more sensitive and robust solution and if I was designing an ultralight, where drag isn't that big a consideration, I'd use a tab for the elevator, and perhaps a bungee in the rudder and aileron circuits if I wanted rudder and roll trim.