You've heard "defense wins championships," "big men win championships," "point guards don't win championships," but the formula I think generally gets the job done is a little different
My parents grew up playing basketball in New York City in the 60's and 70's, and both of their favorite teams from all time are the early '70's Knicks. My mom thinks Walt Frazier is the GOAT (granted, she hasn't really been an NBA fan since about 1977, but the point still stands). With that background, they always taught me when I was a youngin' that the most important part of basketball is passing. I didn't really understand fully what they meant about that when I was 8: I just thought they meant I should work on my give-and-go or something like that. Now that I'm a bit older, I think I understand the type of passing two people who worship those Knicks teams are talking about:
It is the ability to take advantage of the defensive attention you demand in the midrange or post and make the smart, easy play to the open man. This is what Clyde's talking about anytime he mentions that he thinks great players make their teammates better.
Just about all of the all-time greats with whom I have any familiarity-- Jordan, Bird, Shaq, Hakeem, Magic, Duncan--were masters of this. Dirk (finally) exhibited this trait during this year's playoffs and the man got himself a ring doing it. I believe that Phil Jackson has been so successful largely because the triangle opens up passing opportunities for its primary players and allows them to become play makers. I think any great scorer can become a great play maker if he has the intelligence and willingness to make these plays.
Generally, I think this type of play making is more effective in the playoffs than the Steve Nash/ John Stockton/ Chris Paul version of play making where the point guard is very ball dominant and works to set up all his teammates' looks, or the Lebron/ Derrick Rose type of drive-and-kick play making where everything comes to a screeching halt if the defense is successful in taking away the drive. I do not mean to say that point guards don't win championships, because I am a huge fan of Steve Nash and Chris Paul, but I do believe that their teams struggled because the play making was so concentrated in one player. This isn't inherently Nash's and Paul's fault, and it doesn't mean that they can't be major contributors to championship teams; it could just mean that their teammates weren't any good at generating offense.
I've said it before around here, but I think if Carmelo Anthony can add this type of passing to his repertoire, he could be as good as anyone playing right now. Frankly, I will be very disappointed in both him and D'Antoni if next season I do not see the team run its offense through Carmelo and Carmelo make a concerted effort to make the smart passes. That quote by D'Antoni about expecting Carmelo to average close to a triple double every night and seeing Carmelo play some point forward have made me optimistic, though. I would like to see Amar'e improve in this area too, but I do not believe he is as gifted a passer or has the court vision of Carmelo. If Amar'e can just stop doing that thing where he isolates at the left elbow and then runs into three defenders in the paint and instead just pass to the damn cutter , I will happy enough with him.