In this article there is a short list of such incidents. As I said they are rare.
Do citizens (not police officers) with guns ever stop mass shootings?
By Eugene Volokh October 3, 2015
Backers of laws that let pretty much all law-abiding people carry concealed guns in public places often argue that these laws will sometimes enable people to stop mass shootings. Opponents occasionally ask: If that’s so, what examples can one give of civilians armed with guns stopping such shootings? Sometimes, I hear people asking if even one such example can be found, or saying that they haven’t heard of even one such example.
A while back I posted about a few examples, but since then there have been some more, so I thought I’d note them. Naturally, such examples will be rare. Even in states which allow concealed carry, there often aren’t people near a shooting who have a gun on them at the time. Many mass shootings happen in supposedly “gun-free” zones (such as schools, universities, bars, or private property posted with a no-guns sign), in which gun carrying isn’t allowed in many states. And there is no central database of such examples, many of which don’t hit the national media, especially if a gunman is stopped before he shoots many victims. Moreover, at least some examples are ambiguous, because it might be unclear — as you’ll see below — whether the shooter had been planning to kill more people when he was stopped.
Still, for whatever they are worth, here is a list of some such incidents (which deliberately excludes killings stopped by people who were off-duty police officers, or police officers from other jurisdictions, at the time of a shooting, as well as some other cases which struck me as borderline):
https://www.washingtonpost.com/news/volokh-conspiracy/wp/2015/10/03/do-civilians-with-guns-ever-stop-mass-shootings/
Another factor is that mass murders usually pick soft targets which such as gun free zones to carry out their attack.
There are over 1,000,000 residents of Florida who currently have a valid concealed weapons permit but Florida law says you can't legally carry a concealed firearm even with a carry permit into an establishment such as the Orlando nightclub that was just attacked.
However the idea that if only more people start legally carrying concealed handguns everywhere mass murders will end is foolish. Usually the shooter has a far superior weapon and any responsible person would have to be close to the shooter to place an accurate shot that would stop him. The good guy would also have to consider that he might easily injure an innocent person if he missed. Handguns especially the ones usually carried concealed are far more difficult to shoot than what you may believe if you watch movies or TV. Also an individual may be a great shooter on the range but stress and adrenaline cause a his/her skills to diminish considerably.
Legally concealed handguns are most useful as self defense weapons in situations where there are one or two attackers and once the attackers realize their victim is armed they run.
For example my mother back in the 1920's time frame was walking home from work in a rural area after she got off a bus. A man who had been hiding behind some bushes rushed her. She had a small S&W .22 caliber LadySmith revolver in her purse which she drew. She fired two shots over the man's head and he ran.
As a side note she kept that revolver as a souvenir and hid it in a box in a drawer in her bedroom. Of course I found it. I loaded it with the bullets that were in the box. I don't remember ever pulling the trigger but if I had it wouldn't have made a loud noise. My father had wisely removed the firing pin.
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