Watched the entire series a few weeks ago, and this is definitely my answer. Murtaugh and Riggs, total opposites, but you can see how their relationship builds with not only every addition to the movies but with every scene their bond grows stronger. Their funny scenes like the toilet/bomb situation is classic but I love the emotional scene at the end of LW2 when Murtaugh tells Riggs, "You die when I tell you to." I thought that was so powerful and telling in just how far they had come up to that point.
Riggs started as a pain in the ass to Murtaugh and he still was throughout but they grew to respect and care for each other and became like brothers. They had no choice after all these evil people threaten the lives of their families, and in Riggs's case murdered the one he loved dearly that initially sparked his give no fucks attitude to policing. Gibson & Glover were made for these roles together, perfect chemistry. Through Joe Pesci as the funny third wheel and Rene Russo kicking ass and it is a bonus.
btw, I still think Riggs hit that with Murtaugh's daughter! They were doing a little too much touchy feely in this series.