okay, i guess i will go first. My ideas aren't that perfect, but here they are:
Tower- stack cups, using guy wires. does anyone not use this design? lol
Bridge- Two heavy masses (duct tape, misc. balls, cups, etc.) are on either side, leaning away from the other. then there are parallel lines of string connecting them. in the middle of it lies a plate, which is where you put the cup.
Cantilever- I used paper as a counterweight mainly, and made the thing that goes out out of rolled-up paper. again, there is a plate to put the cup and ball on.
Catapult- Okay, my design sucks, and i barely remember any of it... but it basically consists of a triangle made of 3 cups with a tennis ball in each, all on layers of plates. A rubber band goes around 2 of them. Then, there was something with the popsicle sticks, but all i remember is that they were used as a trigger. the ball shot 2 yards if we were lucky. >.>
Bouncer- This design also is not good. I have A pile of paper, a pillar of cups, and 3 bowls with lots of rubber bands around it. I put the bowls on the cups and the cups on the paper. Then i duct taped it all together. Finally, i made a tunnel thing out of paper above the bowl and attached it with popsicle sticks. That way I could drop the balls at the exact same spot. (however, when we used this design at states, the paper thing got crooked D: ) The ball would shoot a foot, but was extremely accurate, unless the paper tunnel thing falls off.
Ramp- This, in my opinion, is my best design. I cut the bottom end of cups, and taped them all together with duct tape, so they made a long tunnel.then i supported it with more cups and paper, and taped it all together so that it looked like a... well... ramp. then at the end I put a small tunnel thing pointing upwards so the ball shot up. I never really even tested this design... so there might me a few errors actually.
All in all, jyc has been pretty much an awesome event. More exited for mission possible tho XD
edit- lol, i think that was my longest post ever. did i spell popsicle right? the spell-check says nay :O