While it wasn't limited to the 1980s, but the Buddy Cop schtick was big during the 1980s. 48 Hours, Miami Vice, Lethal Weapon, Simon & Simon, Tango & Cash, Moonlighting, Remington Steele, Red Heat, and so on. Typically you have a pair of mismatched personalities tossed together and forced to unite to solve a crime. There's often clashes early on which wind down as they get further in to the investigation and start realizing that the other brings something to the table that they don't have.beverly hills cop: the rpg
If you want to see something that nails a lot of 1980s tropes, there's this: