My bike's rear axle is loose, which means that applying any weight causes the back tire to rub against the frame, thus preventing forward locomotion.
...we will see what will be done about this.
*UPDATE* I've determined the problem is the rear axle. Namely, it's in two pieces. I'd be exceptionally proud of my mechanical prowess in finding the problem at all, but I kept wanting to call it a crankshaft, so "prowess" may not be the right word.