Just before I moved, my friend Red made me a Clint/Tasha mix. It's frigging awesome.
I listened to it again last night, and because of this I have developed chunks of headcanon for the two of them that bleed over into the rest of the Avengers, and maybe even a couple other fandoms too. IDEK.
Cut to save your brains should you want to skip it.
1) Contrary to popular belief, Natasha is not a drinker. She doesn't like the feeling of being tipsy or drunk, as it makes her feel less in control of herself. Given her whole experience with the Red Room, this should not come as a surprise, but the only people who know about the Red Room are Fury and Coulson. Clint's got an inkling, but he's not saying anything.
The only time she will drink is when her cover on a mission requires it. On her own time? No.
2) Clint's the drinker. He's a fan of the hard stuff. This is the residue of his time in the circus. Everyone there drank, so he did too. They always seemed to have cheap whiskey on hand for after performances. On occasion, they even had halfway decent vodka.
(This usually happened when they met up with other troupes. One had this family: the Graysons. The kid, Dick, was about Clint's age at the time, and the two of them hung out whenever they crossed paths. Decent guy.)
He doesn't drink to excess anymore -- did enough of that as a teen. Still buys and drinks cheap whiskey out of sheer habit though, particularly after rough missions.
4) The only commanding officer that the two of them respected entirely and trusted implicitly was Coulson. This is saying something, as they went through a few before Fury noticed how damn good Coulson was and pulled him up the ranks.
When Coulson died, Natasha and Clint served as his pallbearers. They weren't supposed to be initially, but are you really going to say no to the two of them when they make that kind of demand?
Tony was another one of the pallbearers. The fourth and final one was Steve.
After the funeral is the only, only, only time that Clint and Natasha ever got absolutely plastered together.
They don't talk about that night.
5) Each of them has a safe house of their own. They will never, ever tell the other about the locations, which the two of them are just fine with. There is an apartment in Lyon, France, that they share though. It's perfect for whenever they're in Europe. Everything's a daytrip away at most, so they can get through their mission (whether as a partnership or individually) and then go recoup in Lyon before returning stateside to report back to SHIELD for debriefing.
6) In answer to the inevitable question, no. Neither of them is going to tell you if they've slept together or not.
7) Clint can speak fluent Iraqi Arabic. He can read it too. Can't write it for shit though. He was posted in Iraq for a longass time -- deep cover mission, if he told you he'd honest-to-God have to kill you, lots of things he'd rather not remember, etc. -- and learning it came in kinda handy. He picked up some of the North Mesopotamian dialect too. Emphasis on some though.
He's taught Natasha how to swear in it, but only did so in exchange for being taught to swear in Russian.
One of his goals in life is to learn how to swear and/or insult people in as many languages as possible.
I'll stop now. Mainly because this will end up going on and on if I don't. Feel free to build off this stuff with me or share your own thoughts on these two, or hell, any of the Avengers -- I love playing with headcanon, as
xenokattz will attest. Awful Awesome things generally result.