The best thing about shotguns is the versatility. There seems to be no limit to what can be shot out of them. Some things might not be advisable like shooting .50 BMG round out of a 12-gauge, others are not dangerous but not very effective.
This experiment lies somewhere in the middle. It does not seem that dangerous, but could possibly damage your gun, but also only mildly effective.
What I really like about this video is the aerodynamic test they put the pennies through. The water method did a pretty good job of predicting what the pennies would actually do when fired.
In this Video TAUFLEDERMAUS, runs the penny rounds through their paces and has some really interesting results.