When my brothers and I were kids, we used to draw basically three superheroes: Batman, Superman, and Spider-Man. Those were the only superheroes we knew, and they had such iconic looks to them. Then, when we were a little bit older, we started to branch out a bit. Thanks to the Batman and X-Men cartoons, we became aware of the DC and Marvel universes.
At this point, we started divvying up the characters. This was necessitated by a couple of things: first, when playing the X-Men game at the arcade, we had to pick different characters. Also, if we were going to pretend to be our favorite characters, we had to be different people for it to make sense. And finally, it allowed for the "Who is cooler?" and "Who would win in a fight?" debates that all nerds live for.
It was at this time, way back in grade school, that Wolverine became my favorite superhero. He was badass, he could fight anybody, he was independent, and he had that badass costume. At the time, I thought that the only "real" Wolverine was the guy in the yellow tiger-striped costume with the blue shoulderpads. I didn't like the "old" brown-and-orange costume (not realizing which one he had started with), but I had a special dislike for depictions of him in his "civilian" garb. That wasn't Wolverine, after all: that was Logan, which amounted to Wolverine in disguise. How could you be a superhero without the costume?
Then, starting around high school but really ar0und my college days, I started moving away from Wolverine. My main reason for this was simple: everyone likes Wolverine. He was far and away the most famous of the X-Men. In fact, it could be argued that he's the only member of the X-Men that most people actually like. It certainly seems that way from the covers Marvel puts out: go to any comic shop and count the number of covers that feature Wolverine and the number that don't. You'll be surprised.
At about this time, I started getting into other superheroes. First, Iron Man. I had been reading The Ultimates, and I really liked that depiction of Tony Stark as a reckless, charming rich guy who decides to make the world a better place before his brain cancer kills him. I liked the idea that Tony Stark is a normal human who fights with his intellect, creating a high-tech suit of armor that he can modify and upgrade as the situation demands, allowing him to defeat enemies by outsmarting and out-building them. All that Wolverine ever did was get mad and stab things! Too bad Civil War came along and made the mainstream version of the character the most hated superhero in Marvel. Then, even worse, I found out that the Ultimates version wasn't as "normal" as I had thought: his body is one large living brain, thanks to his monkey blood. I hate his stupid monkey blood!
Then I liked Deadpool, who was a lot like Wolverine: he had Wolverine's regeneration, he fought with guns AND swords instead of just claws, he was hilariously offbeat, and he was a ninja. Everyone likes ninjas! In fact, I liked Iron Man and Deadpool so much that, when we played through Marvel Ultimate Alliance, those were the two heroes I played with. True fact: we let the computer play Wolverine. Eventually, though, I had to admit to myself that Deadpool was just a surrogate Wolverine.
If you will indulge me a moment, please allow me to geek out about the thing that makes Wolverine the best at what he does: he's a fighter.
That's really what it comes down to. No matter where he is, no matter what he's up against, Wolverine is going to fight it. His adamantium skeleton, razor-sharp claws, and healing factor all mean that he has the ability to put the hurt on the enemy, and he has the staying power to make sure he has the opportunity to do so. It's not only about the ability to take damage and keep fighting, but even moreso it's about his willingness to do so no matter what.
Wolverine is, after all, named after an animal known for fighting anything, despite its small size. The Marvel character, too, has the bloody-minded determination it takes to keep getting up, no matter how many time you're knocked down, and keep getting stuck in. Wolverine exists in a universe full of cosmically powerful beings who can sling around some amazing pyrotechnics. All he has to go up against that is one thing. Make that three things. On each hand. So, six things total. As Ho Chi Minh observed, "If the Tiger does not stop fighting the Elephant, the Elephant will die of exhaustion."
Except in this case the Elephant is a supervillain who can blow up the side of a mountain, and the Tiger is actually a Wolverine.
It's true that Wolverine, like Lobo, has much more potential than actually delivered by most of his comics. The need to shoehorn this loner into a team comic often means that he soon learns the value of teamwork and trusting others, often becoming a father figure for one or more young teammates in the process. And, yes, he wears silly costumes. But no matter how many costumes you put him in, and no matter how many times he tells angsty teens to believe in themselves, he will always be Wolverine.