A 22 will stop a person, but normally it's going to take a day and half, and you'd better hope that nobody has the presence of mind to seek medical attention. An excellent idea would be to have a good knife as a secondary weapon.
The 22lr is meant to be used on small, light animals like rabbits, which weight only about ~15 pounds. A human man, even if he is small and lacking in musculature, can easily be 150 pounds. As Prosser said, that most bad guys tend to be big and tough, they therefore are going to be even more unsuited for a 22 than the 150 pound basement shrimp.
Do you really want to bet your life on a small game/training round? In order to stay alive, you need to win every single time. In order to kill you, they only need to win once.
Handguns are truthfully not great for stopping humans, even the more powerful calibers in expanding configurations are not great quick reliable manstoppers. You also must think about what a person can do when intent upon inflicting harm and coursing with adrenaline, such as in a fight where a gun is pulled on them. On adrenaline, people often report that they didn't even notice that they had been shot until they fell over or until after the fight was over. As was said by my former teacher about when he was shot by a 7.62mm AK, that he just felt like someone had given him a hot shove but he didn't really notice until after the engagement had finished. when he felt a pain in his leg and noticed that blood was soaking his uniform. One of the important things to stopping someone is making them hurt and realize how hurt they are. If a 22 was all that was necessary, then why does the FBI not issue them or recommend them?
A smart man carries the best, most powerful tool he is the most skilled with. A 22 is an inadequate defense against an attacker of the human species. Personal defense is not really an area where you want to skimp on costs; this isn't like using compact fluorescents or taking generics.
Here's a bit of a weight and caliber table
http://www.chuckhawks.com/gun_game.htm