Tony
Leaving you alone and being alone. He also hates black cats.

Steve
Immense power in the wrong hands. He also fears hitting the ones he loves.

Bruce
He fears himself. Also, and know one knows this but you, he is scared of fish. He says they are so creepy when you're swimming and they rub on your feet.

Pietro
He is scared of not being quick when danger crosses your path.

Bucky
He's scared of Hydra finding him and you, he knows they'll torture you until you die and then erase the memories of all the good times you two had together, he doesn't want to forget. He also is jumpy around llamas because they look freaky.

Thor
He is scared of not being able to protect the worlds and is scared of the day ihe might have to kill his brother, Loki.

Clint
He is afraid of missing his target. That's basically it. Nothing really in hinges Clint because he knows that as long as he can hit on target that he can protect you and his team.