Lets see....Craziest thing to do with duct tape...
Ever seen those large foam novelty sombreros? Well during regionals we made one...outta duct tape. If you look at the webcast of the Lone Star regional quarter finals at the 43 min. mark, you can see the announcer wearing it.
http://robotics.nasa.gov/events/webcasts/lonestar.htm
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I have used duct tape to tape a broken toe to an non broken one on a backpacking trip. It wirked really well and kept it realitively painless.
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On a long road trip, in the middle of the west texas desert, we had a radiator hose break. We duct taped the crack closed. When we started the truck, the heat melted the tape and created the perfect seal. We drove the last 550 miles on it.
-Bill B.