This is stuff I wrote for a BLU Spy I was playing over at an RP, but most of it is generic enough that it can be used as general Spy headcanon:
*His closet is full of clothes that he uses for infiltration: formal, casual, uniforms...
*He's sleeping with the RED Scout's mother for the view in her apartment.
*This was, more or less, how he asked: "Sup, I'm a BLU Spy. If you let me take pictures of the nice apartment across from yours I'll give you the most mindblowing sex you can ever imagine."
*Though all he knows of foreign languages are the kinds of basic vocabulary that you could find out of a phrase dictionary, he can imitate the general "sound" of most major non-English languages in a way that it sounds fairly convincing if you're not a native.
*He can imitate voices, accents, and verbal tics almost perfectly.
*He can pull off a fairly convincing crossdress. He goes all the way, too: wig, padding, tucking, shaved legs, the works.
*Most of his campy mannerisms are just to make people uncomfortable. He considers sex another tool in his arsenal; he takes much more pleasure in lying, manipulation, and being a troll in general.
*He treats his teammates depending on how they see themselves. If they're "baww I'm a big giant failure" then he's all supportive Team Dad. If they're "I'm the shit" then he's out to prove that they aren't.
*Since the "Meet the Spy" video, the BLU Soldier's been on pins and needles expecting some kind of payback. The Spy finds it much more amusing to watch the Soldier wait for the other shoe drop.
*He does, however, troll both BLU Soldier and RED Demo as each other.
*The first time he sapped a sentry, he totally jizzed in his pants.
*Those are HIS own custom-tailored silk suits (he made them himself with a super high end sewing machine) that he wears, not BLU-issued.
*When he uses his default knife, he carries extra ones hidden all over his person because it's crap and it breaks/malfunctions a lot.
*He's convinced the BLU Demoman that Spy Crabs and Tenta-Spies are actual creatures.
*Most of his "CLASSY MOTHERFUCKER" trappings are faked for the sake of his persona. He's not a snob for anything except foreign cigarettes, something that actually happened by pure accident--he'd gotten some in return for a favor once upon a time, and he fell in love with them at first smoke.
*He is surprisingly good at free-running despite his smoking habit.
Similarly, here is some RED Sniper headcanon:
* Still attends reunions for his high school and army unit.
* He sneaks out into the wilderness and eats off the land every so often.
* Doesn't keep pets often, but if/when he does, he prefers non-standard stuff: reptiles, spiders, saltwater creatures...
* He lists them all as "emergency food supply" so they'll be okayed by RED.
* He made Ol'Snaggletooth and Darwin's Danger Shield himself. His Dad was still disappointed because the Sniper hunted a male croc out of season, not a nesting female croc like a Real Ozzie Bloke would.
* Sniper!Mum isn't as demanding as Dad is (he's her baby after all), though of course she still does expect him to live up to Ozzie standards. And she wants grandkids.
* In TF2-verse, drop bears, bunyips, and jackaroos are all real animals. The Sniper's gone after them all, to varying degrees of success.
* His parents own a ranch that does fairly well for itself, but the Sniper still sends home money anyway (that Mom is just saving up in an account).
* Can identify edible plants and fungi at a glance.
* Is willing to try anything at least a few times, but has a fairly narrow range of foods he truly likes and won't get tired of eating. (Yes, Vegemite is one of those things.)
* Is a total gun nut. Collects guns, facts about guns, etc.
* Also tends to be a packrat due to his philosophy of being prepared for the worst. Keeps emergency stashes of supplies everywhere.
* In his travels if he sees a place he likes, he'll buy it, fix it up, and then rent it out, or give it the illusion of being occupied so he can use it as a safe house in case of whatever.
* In addition to his safe houses, he has quite a few alternate plans in case the Sniper thing doesn't pan out.
* Tends to be the most proactive of his teammates when it comes to chores and the organization thereof. (Prefers doing the laundry, but is willing to do everything else.)
* In battle, he won't camp unless it's a really good spot that nets him a lot of kills without having to worry about getting killed. Prefers non-traditional shooting lanes, and depending on the map type, will even be on or near the front lines.
* Is totally not the loner type. He hangs out with his teammates quite a bit after hours: will play catch with Scouts, assist Engineers in tinkering, take up prep duty for meals that need to be cooked, etc.
* This should really be obvious, but he's not really that much saner than his teammates. It's just that being surrounded by the likes of those nutters means he can pretend to have things together. (When he thinks he's alone, he's much nastier.)
* Ironically, his sense of direction is pretty terrible; he can deduce the cardinal directions from local cues and all, but he relies very heavily on maps (or the good old method of "going in one direction until you reach a dead end, then retrace your steps") for his pathfinding.
* He's not assigned to any one group of people for long, as he's always being called to assist other RED teams, so he's seen the gamut of play levels and styles, from the super serious pros to the hat-obsessed newbies.