In the fastest street tire heads up classes, they regularly and successfully run a 10" tire on a 15" wide rim with bead locks. The reason is to make the entire tread stay on the ground and not round and grow at speed like tires do when the rim is narrower than the tire as Dparker noted earlier. A narrow rim is not the best choice but as long as the side effects don't bother you you can run the rim narrower than the tire. The street tire guys do the exact opposite proportions for the best traction for there application.
The only reason to do this intentionally, is to keep a limited tire width usually by rules, planted, where a wider tire is needed.
P.S. throw the tubes out too......