It ain't copaganda if it's... uhm... weeelll... okay... it is copaganda, but what're you gonna do, I'm a child of the 80s.
Two people. Conflicting personalities. One wild, hot-tempered, iconoclastic. The other, level headed. Working together, often forced into a partnership, to defeat the criminal element, and sometimes, sometimes, maybe even learn a thing or two from each other along the way.
While most often action comedies, there are also serious efforts done with this trope, I'm including all of it. I'm also including the buddy cop-dog subgenra, because what is a dog, if not The Man's best friend.