I came out of the movie 'shipping Bruce/Natasha on OTP levels pretty much only matched by Michael/Selene, who are, y'know, canon, and their being together is kinda the point of the story. (Yes, I have noticed the extremely direct parallels between the two 'ships. Apparently whatever you call that dynamic, it works for me.)
The rest of fandom apparently came away 'shipping Bruce/Tony. And there's been a fair amount of Clint/Natasha, too.
I can definitely see where people got that - for Bruce/Tony, because Tony definitely reached out to Bruce, and was sincere about it, and Tony kinda doesn't do that much. And the Hulk saves his life when he's falling, and yeah, there was bonding there. And Clint and Natasha, similarly - clear that they matter to each other, a lot. Probably doesn't hurt that they've been a couple in comic canon.
But, regardless that I can see the sense in these pairings, they are not the OTP and thus not what I want. This is me admitting my bias here. But . . . with no insult intended to those who write or read the above pairings, and full cognizance of the fact that yeah, I'm pairing off random team members and seeing romantic vibes where canon did not intend them, too . . . but I loved the dynamic presented for Bruce and Tony in the movie, just as presented, and I think maybe because canon has presented Tony as such a completely manwhore that it was kinda sweet and nice to see him reaching out to someone who was explicitly not a sex object (and also of no use to him any other way, either). It was interesting to see Tony react to someone in a way that was very, "Oh, hey - equal! Maybe I could like you." As opposed to his "I want one" reaction to Natasha.
. . . none of which is to say that you can't take that and develop it into a more intimate relationship, but I get wistful for stories about friendship, and sometimes fandom's SLASH ALL THE THINGS reflex makes me roll my eyes a bit.
There weren't too many friendship fics immediately, but they're starting to crop up more (or maybe I'm finding them), and I'm loving them dearly. I may do a rec post.
. . . I am not sure this post had a coherent point, except that I want to get back into fandom and livejournal and meta and talking about these things, because I can has a fandom again, and this is fun, and I have missed it.
PS: anybody know where I can find Avengers icons? I do not presently have the software to make my own.