The buddy cop movie is a standard in cinema these days. The contrast between two very different police partners is a template for tension, comedy, or a complementary system that makes the whole more than the sum of its parts. And the more diverse the two are, the better, because you know they'll end up either bonded for life by their adventures, or else they'll kill each other. Which police duo is your favorite? I was always partial to Cagney and Lacey, but that's TV. See who made the list of great cinematic police partners (with video evidence) at TVOM.
As for the list's omissions, no Starsky and Hutch (movie version, fratpack gold), no Stakeout (a classic), no RUSH HOUR (WTF!!!!), no Turner and Hooch (does it count, tho?), no Dragnet (movie version, one of my personal favorites!), no Hot Fuzz (what an omission!), no Se7en (I have no words!).