Scans_Daily

I think for me, I would probably say Tintin and Captain Haddock. As ficticons pointed out above, Tintin also has a very deep and beautiful friendship with Chang Chon-Chen, but A: we really only see examples of it in two of the books, and B: the two are too much alike for it to be really interesting; both are so pure of heart that one half expects them to rise into the sky in a beam of light at any moment.
The Tintin/Haddock friendship, though, is a really interesting one. On the one hand, you've got Tintin, boy adventurer, gutsy, adventurous, clean-cut; on the other, you've got Captain Archibald Haddock, middle-aged retired sea captain, semi-professional drunkard, member of the country gentry, and general foul-mouthed klutz. The two have almost nothing in common, yet there is a deep connection between the two of them. Tintin gets a bit exasperated at the Captain at times, yet clearly depends on him as an emotional anchor and sounding board, if nothing else, and is obviously distraught on the really rather frequent occasions when he thinks his friend has bought the farm. Haddock, on the other hand, is absolutely devoted to Tintin for a clear and simple reason - he saved his life. If it weren't for him, he'd still be a pathetic boozehound drinking his life away as the pawn of a ruthless criminal. Tintin rescued him from all that, gave him control of his life back, and in the process gained a firm friend and partner in adventure. Haddock may scoff at what he sees as Tintin's naivete, he may grumble at being dragged into yet another adventure when all he wants is to stay home and read the paper, but there is never any doubt that where one goes, so goes the other - the one exception to this is in 'Tintin and the Picaros', where things take a pretty dramatic downward turn for the series in general. He's Tintin's right-hand man, and would sacrifice his life for him without the slightest hesitation - view the scene in 'Tintin and Tibet' where he prepares to cut the rope holding the two of them together. There's not a hint of doubt, only grim determination - his friend will die unless he dies first, so he might as well get it over with. If there has ever been a deeper, yet more unlikely friendship in comics, I've yet to see it.
Runner-ups, I suppose, would include one similar to yours - Blue Beetle and the Question. I know, I know, they only teamed up a few times, but they really clicked when they did, as is shown by their expies in 'Watchmen'. I continue to hold out hope that the current versions will have a team-up at some point. Also, the Newsboy Legion - they're a pretty tight group.