[Jared]

Worm gears are pretty good for this type of application.

We used a two start worm on our climber with decent success. We used a 2 start 16 pitch worm and a 20 tooth worm gear. We must have climbed our practice tower hundreds of times with the setup (2 CIMs direct driving the worm) and we had no issues.

Worm gears aren't indestructible though. We broke two, one bronze, one steel, once we increased our climber to 3 CIMs and doubled the speed.

I think you can do better on efficiency than the previous poster has mentioned.
Our climber, which was two belts, the worm reduction described above, two #25 chains, and a 5 start lead screw, and we saw over 50% efficiency (measured by the amount of time it took the robot to lift itself).

Making sure the worm/worm gear are in the exact right spot is very important. We added .002" extra to the center to center like we do with spur gears. Also, make sure you put plenty of grease on the gears.