We used worm gears in our robot last year with great success. We didn't experience a single failure in our drive system. Although, I suspect the low friction surface in last years game made it very easy on the drives
The gears we used were a bit unusual as far as worm gears go, since the worm had 6 starts. This meant that the reduction was fairly low (5:1 I think), and the gears were back drivable. We obtained the gears by taking apart a pair of industrial gearhead motors that came from a surplus shop. We got several sets of gears for quite a low cost.
As others have mentioned, precisely aligning the gears is key. We machined a housing for the worm with bearings supporting the shaft on both ends. Then a shaft coupler connected to the CIM motor above. The coupler makes things less compact than directly mounting the worm to the motor, but it allows for misalignment, and prevents axial loads from being transferred to the motor bearings. It also simplifies changing the motor.
For lubrication we used grease, and the gears were enclosed with a housing we built. A small hole at the top of the housing allowed re-greasing with a syringe.
Anyway, I have attached a couple pictures of our design. If anyone is interested, I can send Inventor files.
Rob