Wolverine is called the best at what he does, but that something happens to be killing people, and he's put that particular set of skills to use a lot over the years.
In fact, he's left such a pile of bodies in his wake that Mr. Sunday Movies and Oceansparks counted them all up for us and created this nifty Wolverine Movie Kill Count Supercut, which totals all of the kills he either directly made or indirectly caused (like blowing up a helicopter that killed two people for example). The supercut features all of Hugh Jackman's X-Universe appearances, including the original X-Men, X2: X-Men United, X-Men: The Last Stand, X-Men Origins: Wolverine, X-Men: First Class, and X-Men: Days of Future Past.
A few things to note about the count (which comes out to 90 people). It only includes the movies, as in the comics it has to be in the high thousands, and even though X-Men: Days of Future Past reworked the timeline, the kills he made in the original three movies (including Phoneix from X-Men: The Last Stand) still count.
That count isn't final, however, as the star still has one more Wolverine solo outing before he hangs up the claws for good. The rumor is that the film will involve X-23 in some way and that it could incorporate the Old Man Logan storyline from the comics. If that's the case, expect that kill count to go up exponentially, as the character takes on just about everyone at some point (save for his buddy Hawkeye) in that storyline.