From kid’s shows - Bear from the show Franklin
When our daughter used to watch this show, DH and I used to comment a lot “Man, I wish I had a friend like Bear!” 
Does anyone remember the movie Ran? Japanese warlords, etc. The was a character named Tango who was loyal to his “master” no matter what. It was kind of a one way loyalty, though. I’ve always said that if I ever got a dog that would be his name. I, however, would be loyal to MY Tango. Nearly 30 years later and still no dog.
Disney made an animated version - The Black Cauldron - but it’s considered one of their weakest. It’s available on DVD if you want to watch it.
How about Riggs and Murtagh?
Benjamin Janvier and Hannibal Sefton from Barbara Hambly’s A Free Man of Color series.
Ben is the eponymous free man of color living in antebellum New Orleans. He is a classically trained musician and a surgeon, and he is constantly being called on to help with one mystery or another. Hannibal Sefton is an opium-addicted consumptive, a member of the Anglo-Irish aristocracy, who abandoned his life twenty-five years previously, and the only thing he took was the 100 guinea violin he can play well enough to make angels weep. Hannibal can go where a black man can’t, and Ben has the fortitude and foresight to look out for Hannibal when Hannibal can’t look out for himself.
Nicholas Nickleby and Smike.
Dr. Heinz Doofenshmirtz and Perry/Agent P? They’re relationship is quite complex; they don’t try to hurt, maim, or kill eachother just thwart and capture. They’ve actually saved eachother’s lives several times.