Thor
Thor and Loki would romp and run around Asgard, regardless of what they were to do by their parents. Frigga- inevitably- would send piles of clothes to her servants to clean dirt, plants, and fur out of. If the clothes were salvageable.
So Loki and Thor would lay on the grass by the fountain, completely nude, soaking up the sun's warmth. Frigga would shake her head and laugh at their antics, eventually hauling them- one under each arm- to get some clothes on.
Steve
Steve was always polite, and it showed even in his sleep.
When he was the one being protected, Bucky would hold him and keep him warm. The feeling of his brother (not in blood, but they might as well have been) having his back, embracing him, would keep him hoping that tomorrow would be better.
When he joined the Army, he didn't change his heart- just the body it was contained in. After that, he was the one to hold Bucky in the cold. When he lost Bucky, he felt cold again.
Natasha
When she was a child- before red covered her eyes and her hands- her babushka would run her hands through Natasha's hair. Natasha always loved cats- their agility, grace, and power entranced her into acting like them.
Because she was small for her age, Natasha could curl up on her babushka's lap and allow her warm, loving fingers to lull her to sleep. The warm foods she'd make would make Natasha feel strong.
When Natasha witnessed her murder, she became a cat and went on the prowl. Her claws are always at the ready, even when she's at rest.
The nickname "The Black Widow" wouldn't come until she lost her first husband.
Tony
Tony was alone a lot, so he didn't have to worry about sharing.
He never slept between his parents, never had sleepovers, and never had pets. The bed always held him, and him alone. He'd spread out, like a bear protecting it's territory. Tony had always been reckless- whether for attention or lack of care, no one asked- and so his sprawled sleep pattern was to be expected.
Of course, those close to him know that he just wants to know he's not alone. He wants someone to wrap his arms around. He wants to know that he's not throwing his life away for nothing.
Bruce
Bruce had never been able to sleep well without external stimuli. As a child, the pain in his head and body kept him awake, crying for the hurt to go away. As a teenager, Bruce focused on his schooling (having started college in his mid-teens). For most of his adult life, Bruce couldn't afford to become dead to the world for fear that he'd never wake up.
Back then, Hulk scared him. Of course, he and Hulk were on better terms, but the fear of capture, taking up space, and being in pain would force Bruce (and Hulk, if he was out) to curl up into a knot before falling asleep.
Even their dreams were haunted by the sounds of tanks, tests, and blood on the pavement.
So they'd cry. Even when surrounded by people who cared about them, Bruce would fall into a forced sleep, brought on by exhaustion and the sheer volume of food needed to replenish his depraved body.
Clint
Clint was used to being the target of bullies, but Barney always helped him out. To help out, Clint would stand guard of his brother and look out for muggers and other dangerous people.
Barney would thank him in the morning, even when Clint fell asleep at his "post".
Eventually, Clint was alone.
He'd been broken again, but he couldn't be dragged into the nothingness of sleep. His eyes always kept watch, just in case Barney came back. He didn't know he slept with his eyes open until Coulson approached him after training one day and told him that he'd done a great job keeping watch.
To remind himself that he's still human, though, he'll scare people (especially Tony) by sleeping with his eyes open in random places. It helps.