Nate, Teddy, and Francis from the newspaper comic, recently turned into a series of kids' books, Big Nate.
Calvin and Hobbes: The title protagonists, who even go to the point of violently beating each other up. This seems like a trend in Calvin's relationships, since he also has undeveloped Slap-Slap-Kiss with Susie.
Peanuts: The entire cast takes part in this to some degree, with Charlie Brown of course receiving the brunt of it, but despite all the fighting between them they are quite a close knit group.
What about Snoopy and Woodstock?
Pearls Before Swine's Rat and Pig. Rat will abuse Pig to the point of literally throwing him under a bus, but underneath it all he does care for his little buddy, as evidenced by one strip where sat by an unconscious Pig's hospital bed.
In one Thimble Theater Poopdeck Pappy, the father of Popeye, says that the reason he made his one friend, the diminutive "Pookie" Jones, is because they used to be fierce enemies until one day Pappy suddenly considered Pookie and realized that he simply wasn't worth hating, so he made friends instead. Upon hearing this Pookie flies into a rage. Pappy holds him away At Arm's Length as he punches at him furiously, chuckling, "Ain't he cute?"
Tiger often shows the title character engaging in schoolboy brawls with his buddy, Hugo.