Hugging
The first time Steve hugged Tony, it was a hug of relief that Tony had survived the fall of the was after the Avengers had all moved into Avengers Tower a week after the Battle of New York, and Tony had gotten injured and almost fallen off the building. They had just won the fight, all the bad guys were in custody, and they were exhausted. Tony apparently had been tired enough to lose his grip on a handhold, and was too close to the ground, only about twenty feet up, to right himself and fly, so he landed flat on his back.
Steve had witnessed his fall and, as the closest Avenger, ran to his side to see if he was alright. Tony, breathless from having the wind knocked out of him, had taken his suit off, so he would be able to stretch out and get his breath back, and was sitting in the back she'll of his suit.
Steve went to his knees beside him and pulled him into his arms, Tony immediately stiffening and pulling away, hopping to his feet breathing hard, and eyes wild, but not from the fall.
Without a word, Tony turned away, not even bothering to get his suit. He knew Fury wouldn't even try to keep it, and would have one of his lackeys deliver it back to Avengers Tower.
Natasha, who had watched the entire exchange, walked up to Steve.
"Every since he got back from the desert, he hasn't let anyone besides Pepper and his robots touch him. He won't even let Medical do anything to him," she explained gently.
Steve replied without letting his eyes leave the still retreating man, "Do you thing he will let someone else?"
She laughed, remembering, "He let me put his watch on him once. He has to be able to trust the person. Don't ever touch him. Let him do the touching. Now that him and Pepper are no longer together, he doesn't let anyone touch."
Steve heard Natasha turn and walk away, leaving the curious man to watch the other one, hoping there was something he could do to help.
Two weeks later, all the Avengers, save for Tony and Thor, the latter of which was visiting Jane, were all gathered in the movie room in A enters Tower. Clint and Phil were a mess of limbs and throw blankets of one of the smaller sofas. Natasha was at one end of the other smaller sofas laying across the whole thing, using Bruce as a pillow, while he carded his fingers through her hair.
Steve had the large sofa to himself, but chose to sit on one end of it, arm thrown across the back, sitting slumped with his feet on the coffee table.
Tony walked in, yawning, and shirt with grease stains all over his white tank top. He looked at the seating options, then chose to sit next to Steve, not touching him, but still where Steve's arm was behind him. Once he settled, they all turned back to the movie playing on the screen.
Steve felt Tony shiver once, then the smaller man shifted a little bit closer to the soldier, almost as if unconsciously. It happened twice more, Tony still not touching Steve, before Steve slowly reached towards the ground off to the side of the sofa, and plucked a blanket from the small pile there. He held it out to Tony, the genius taking it and throwing it over both of them, shocking Steve, and then scooting himself closer to Steve, who was like a human furnace.
Steve let his arm drop from the back of the couch to drape over Tonys still cold shoulders. Tony sighed in content, finally warming up after having to cool his lab down a lot for an experiment, before immersing himself in the movie. Steve looked toward Natasha, who had watched to entire scene, before giving Steve a smirk. He had managed to gain Tony's trust, even more fully than she had ever been able to.