Oooh, that's a very good question -one I could expound upon for ages (though I'll try to save you guys the ten-thousand word essay here). xD
I, personally, do ship John and Sherlock, but not in the way the vast majority of people seem to. I see them more in an asexual (but not aromantic) relationship, because Sherlock Holmes (both in the books and show) has always struck me as asexual. But, they definitely have the potential for a romantic relationship -as you pointed out, Bronwyn, they practically ship themselves! XD Sherlock definitely loves John (whether or not he's in love, which, in my opinion, he is). I mean, he is absolutely intolerable towards everyone else -they can't stand him, and he can't stand them. But, then comes along John Watson, a man who not only puts up with him, but appreciates him, pays him compliments and cares for him. Soon after they meet eachother in the show, Sherlock explains to John how he deduced everything about him at their first meeting. John replies with, "That was... amazing." And, you can tell Sherlock is truly caught off-guard by that. So much so that he feels the need to validate it. Because, people don't pay him compliments often -in fact, they apparently reply more along the lines of 'piss off'.
And, even if one doesn't ship them, you can't deny the fact that they are made for eachother. They're soulmates, simple as that. Whether or not they're in a romantic, sexual, or purely platonic relationship, they are soulmates. Joined at the hip -two halves to a whole. Sherlock-and-John. <3