I find that the chemistry between the characters/actors in that particular sub-genre has a special quality which you just can't often get in other films or TV shows. And this doesn't just apply to the two leads.
For instance, with the Lethal Weapon films, not only is the relationship between Riggs and Murtaugh what keeps the series from getting stale (imo, I guess), but by the fourth installment there's a great sense of... family? I don't know. Same goes for Miami Vice, only that's for five seasons!
I'm tired.