In regards to 1425's Worm Drive - I have been the mechanical student leader this past season, and the drive train and gearboxes were almost entirely of my own design (minus some helpful advise from mentors).
We used a worm drive setup with 2 small CIM's per side geared directly to the shaft of the center wheel, then chain driven out to the corners of a 6wd setup. (traditional 6wd, w/ center wheels lowered 1/8") There's a couple good overhead shots of our practice robot's drivebase here, for reference:
http://www.putfile.com/pic.php?img=4690741
There were a few reasons we went with the worm gear setup. First it allowed us to get a complete reduction out of one set of gears, not multiple stages of reduction. It also relocated the motors to be alongside the outer chains and frame rails instead of taking up all the space in the middle of the robot. The worm drive is definitely more resistant to backdriving, and never once were we pushed without purposely allowing ourselves to be pushed (we didn't exactly go around pushing ALL the other robots - with a single speed its always a matter of balancing speed and power to get a competitive mix, although more than once this season we pushed other robots sideways). The particular characteristics of our setup were not most ideally suited for anti-backdriving - instead the specs of the gears favored higher efficiency, but it was notably resistant to pushing. It was our first experience with both a custom frame and gearbox, outside of that provided in the kit - and plenty of lessons were learned as a result. However I can say that we never once had our drivetrain fail in competition - we attended 3 regionals and championships this year, totaling an estimated 50 rounds.
First I'll describe the specifics of our setup, then I'll get into some of the lessons learned and future tips.
The system had 2 small CIM's facing one another, connected to either end of the shaft with the worm on it (visible in this picture
http://www.chiefdelphi.com/media/photos/26656). That is a hardened steel quad thread worm driving a 60 tooth brass worm gear, for a total reduction of 15:1. The quad thread is MUCH more efficient than single thread worm gears, and a fair amount more efficient than double thread worm gears - but it is also much more uncommon. A quad thread is pretty much halfway between a worm gear and a helical gear, and it took three different suppliers before we found one with 2 gears in stock and willing to make us 4 more within a month w/o additional costs. The worm gear (the lower, larger one on the output shaft) is brass, again due to efficiency. This was our drivetrain, and we didn't want to be loosing power frivolously - I actually ran through MANY equations months ago to estimate the efficiency of our setup, and came up with ~86%, which isn't bad at all - especially compared to this year's kit gearboxes, which yield ~72% efficiency. We were careful to use shaft couplers between the motors and worm shaft, to allow for misalignment, as well as tapered roller bearings to take the thrust load of the worm. We spec'd in .015" engagement slop between the gears, which entirely prevented any interference binding.
We did enough things right that this gearbox was a complete success this year, but there is plenty of room for improvement in the future. For one - don't just design the system based on gear specs in catalogs - before you get too deep, contact a supplier to make sure you can get the gears for a reasonable price. As I mentioned, it took three suppliers to find the gears we needed, and this gearbox nearly didn't happen as a result. The first supplier, whose catalog I had designed based on, told us upon calling that they had never manufactured that gear before and it was going to be over $350 apice - we eventually bought them from Boston gear for ~$110 ($75 for the brass worm gear, and $35 for the worm). Secondly - Make sure to take thrust loads into consideration - worm gears, unlike spur gears, generate thrust along the shaft of both the driving and driven sides. We supported the driving side with tapered bearings. We did not, however, adequately plan for our worm gear's attachment to the output shaft, and all season long we were hassling with set screws when we should have broached our gear and gone with a keyway. After set screws in both of our practice robot's transmissions failed, we eventually drilled and put a hardened bolt through the output shaft to secure the worm gear - not the ideal solution, but a decent fix. (this problem was not just due to thrust loading, but it was definitely made worse by it)
Outside of this, as long as you carefully design out what you wish to make and you have the means to purchase and fabricate all the necessary parts, then you should be fine going with a worm drive. However, as others have mentioned, there aren't always easy fixes if the system fails - so keep this in mind. (we always had spare worm gears with us, just in case one ever failed) Also, if you don't already have it - try and seek out experienced mentors to offer assistance and advice. Nearly all the design was my own, but without mentors peering over my work and making suggestions, it would not have turned out as well as it did.
Sorry for the long post, but I was trying to be thorough. Let me know if you have any additional/more specific questions - I'd be glad to give my input from experience.
- Jeff