Stealing Bitcoins the Hard(est) Way

It seems to come up every month or two on bitcointalk, IRC or any other place where newbie Bitcoiners congregate. Someone finds out that there are a finite number of Bitcoin addresses that can exist, that the addresses are chosen randomly and that there are no safeguards in place to stop someone from randomly generating the same address as someone else and steal all of the coins at that address. All of the above is true, of course, and it is technically possible to steal someone's address and run away with their coins, but only in the same sense that it's possible for one person to get hit by lighting 7 times and survive. Actually, no - even rarer since that's actually happened and this variety of Bitcoin theft never has.