[FourPenguins]

This year we used timing belt in our lifting mechanism. We used polycarbonate pulleys with aluminum hubs. We ended up having to make new, larger hubs after they stripped, but we could have prevented that with some screws through the pulley and into the hub (they were also weakened by machining.)
As far as material, urethane and rubber belts are both very strong and can be purchased with kevlar or fiberglass belting from McMaster-Carr. I've never heard of one breaking in a FIRST robot (not to say it can't happen).
If you're using pulleys/belts, a few things to keep in mind:
1. Find the torque/speed ratings of the belt you're using. Different pitches can take different amounts of torque. You can find this information in The Machinery's Handbook, or probably somewhere on the intertubes.
2. Make sure that your belt is tensioned properly. This can be tricky, especially since it stretches a small amount as it wears in. Adjustable tensioners are useful here.
3. Maximize wrap!!!! Since belt depends more on friction than chain (even timing belt) you want as much wrap as possible.