Martin Chuzzlewit and Mark Tapley, in their unlucky American venture – though if I’d been Martin, I’d probably have bashed Mark’s head in when he came out with his “we need to be cheerful” thing for about the thousandth time.
I’m surprised that no one has mentioned:
Tom and Huck
Huck and Jim
Huck had made up his mind that he would literally go to Hell to save Jim.
Three pages and no Calvin and Hobbes?
You took the words out of my mouth as I was reading the post. Well, you said it better then would have. I was just going to say something like “That’s only because Patrick’s an idiot, he’s not hurting Spongebob on purpose, he’s being the best friend he can be to him”.
Fred Colon and Nobby Nobbs
John Alpha & Wulf.
Walt Longmire and Henry Standing Bear
Yep. But the DiniVerse, Justice-League Bats & Supes also work. That Bruce loves Clark while simultaneously thinking he’s an idiot.
Or even Bats & Supes of – let me think – that storyline when Bruce Wayne was on the run for a murder he didn’t commit. Batman essentially abandoned the Wayne identity (having long since made preparations for since an eventuality), and Superman comes to Gotham to call him on not working to clear his name. Their conversation on the issue makes it clear that Clark loves Bruce, even though he thinks Bruce is all kinds of fucked in the head.
Will and Grace.
It’s complicated.
This is kind of a trope in modern crime fiction. You have the detective (who is kind of badass), and there is the enigmatic friend (who is a total badass) who can:
A:) Do the things that the main character can’t or won’t do
B:) Assist the main character in things that may or may not be legal
c:) Talk the main character into doing things that they normally would not do
So, along with Spencer and Hawk, we end up with:
Hap Collins and Leonard Pine
Elvis Cole and Joe Pike
Myron Bolitar and Windsor Horne Lockwood III
Patrick Kenzie, Angie Gennaro and Bubba
“I’m getting too old for this shit!”
Dusty and Lefty
Dead-Eye Dick and Mexican Pete
Belkar and the Scruffinator
Possibly another pair in that category – Matt Scudder and Mick Ballou? – the majority of their interaction, admittedly, is chatting together and bouncing ideas off each other, but at times it involves extra-legal doings.
No villains? Most villains are such jerks they don’t get close friends, but I always like the occasional trophe of the super devoted henchman. It’s one thing to be buddies with a guy that’s trying to save the world, but to go through thick and thin with a nutcase that’s up to no good and constantly getting his butt kicked by the hero?, that’s love. Michaletto and Cesare Borgias, Joker and Harley Quinn (granted they’re more then friends), Orochimaru and Kabuto, Zanatos and…err…his henchmans name escapes me, but the main villains from Gargoyles.
The RED Demoman and the BLU Soldier from Team Fortress 2, at least before the Administrator ruined their friendship. Though hopefully they’re reconciled now that RED and BLU have teamed up to fight robots.
…yes, I think the auxiliary comics/videos/blog posts that get released with the updates are totally canon unless Valve explicitly says otherwise, why do you ask? 
Scully and Mulder?
Caliban and Niko
Dresden and Murphy were mentioned but I would also say Dresden and Carpenters.
Brisco and Lord Bowler (I want to put the horse but that would be one sided!)
Pete and Myka?
Nat and Dan from Little Men. They are directly compared to Damon and Pythias.
Luvvy and Agatha from Luvvy and the Girls.
In the Forest and Little Bear from The Indians of New Jersey: Dickon Among the Lenapes.