Favorite non-sexual relationship (including asexual romantic relationships)
This is a tricky one. The first thing that springs to mind is the relationship between Commander Samuel Vimes of the Watch and Lord Vetinari, Patrician of Ankh-Morpork, in the Discworld books. The second is the one between Harry Dresden and the spirit Bob (he has an actual name, but as he’s an air spirit, it’s not really pronounceable by humans).
Both are borderline frenemy relationships, for which I have a definite weakness. Bob is essentially Harry’s captive — he gets Harry information, and has a vast store of his own knowledge. When Harry sends him out info-gathering, he has to be very, very clear or Bob will take the opportunity to hang out in strip clubs (he has a serious facination with human sex, in spite of lacking the necessary equipment to engage in it himself). There’s a real affection there, though. When it looks like Bob has been destroyed, or at least had his brain wiped, Harry is distressed for reasons beyond the loss of his best assistant.
With Vimes and Vetinari, things are even more complicated. Both men love the city they serve, but they are very different people and tend to get on one another’s nerves. Plus, Vetinari is highly intelligent and knows exactly how to wind Vimes up and point him in the direction he wants him to go, which Vimes finds aggravating. He can’t resist, though, because part of Vetinari’s brilliance is pointing the fellow at people he can’t help wanting to take down. Vimes takes a certain pleasure in annoying Vetinari whenever possible, which is frequently. There’s a very real respect between the two men, however. Some fans even go so far as to speculate that Vetinari is grooming Vimes as a successor.