Vigilantism allows people to put the value of other lives over the value of the law, the law cannot always protect people but people can protect themselves and others, vigilantism allows people to see hope in the world and it directs people to good over evil, the government can be corrupt or just not there for the people, so let the people be there for themselves.
In some situations I think you could argue that vigilantism is not a bad outcome. There are many cases in which the justice system very obviously falls apart. This isn't something that only happens in super hero comics and episodes of Law & Order. Of course, it does come with a very serious risk.
I believe that vigilantism can never be justified. Taking the law into your own hands in an attempt to find justice is just plain wrong. If everyone who ever felt they had been wronged did that we would live in a barbaric society. We should let law enforcement and the judicial system take care of the crimes that happen in the world.