I know this question is a bit subtle, but let me elaborate it.
In all the canons I have read or seen, Spider-Man swings over the city and whenever wherever he sees the smallest of crimes happening or a person in trouble, he jumps into the situation to save them, be it a jaywalker on the street about to be hit by a vehicle, a mugging taking place in a dark alley, small robberies, etc.
But from what I have seen or read about Wolverine, he is most of the time associated with a team. So basically, he undertakes the missions of that team under the orders of a leader.
In other cases, trouble comes searching for him. He gets involved in action, adventure or fights which directly affect him or people close to him.
In yet other cases, Wolverine has jumped into the situation to help the victim because the victim had once helped Wolverine in some way or other. He just goes back to repay him/her.
In one case, in The Ultimate Spiderman animated series, Wolverine is chasing Sabretooth or something like that. During this, he comes across Spider-Man trying to help people hypnotized by some bad guy with hypnotic orb on his forehead. So he just jumps in the situation to help Spidey and save the day. But basically, he never found the problem himself: it was coincidence that while undertaking his personal mission, he came across it.
I have never read or seen any incident where Wolverine himself goes around randomly to find and fight bad guys or to help innocent people.
Are there any such events in the Marvel universe?