Magnus is a hugger, obviously. It's actually a bit of a problem at the beginning of the mission, before they get to know each other and before Magnus becomes more familiar with the idea of personal space. He quickly learns to ask before tackling someone, and he mostly remembers--except when he's excited, or when one of them has just come back from being dead for a long time. And he learns to be more gentle. He becomes very good at knowing when one of the others needs comfort.
Lup gives the best hugs. Where Magnus's hugs are exuberant and enveloping, Lup's are just like her: warm and compassionate and safe. She always asks first, though as the cycles go on, she stops having to ask with words.
Barry likes hugs, but he doesn't usually initiate them. The others learn the signs for when he needs physical affection, though, and he doesn't hardly need to ask, anymore, whenever he needs one. And if any of the others ask, he gives one without question.
Taako says he doesn't do hugs, but what he means is that he only does hugs with people he trusts. For a long time, that's only Lup. The first time he accepts a hug from Magnus, Magnus is so surprised that Taako has to hug him first.
Lucretia wasn't used to hugs before the Century. She never used to be close enough to anyone to have more physical contact than a firm handshake. But she's learned, over the cycles, from Lup and Barry and Magnus. Her physical affection is quieter, like her: heads leaned on shoulders, a hand slipped through an elbow on a walk. Hugs are rarer, and never taken for granted.
Merle doesn't mind hugs, but he doesn't seek them out. He's more likely to give a pat on the hip, reach out to Magnus or Lup for a fist bump. And in hard times, the others can always rely on Merle to appear with a bottle of something good he's saved and a kind word, to sit with them and keep them company.
Davenport doesn't do hugs. It's just not his bag. It's never been a problem; in the beginning even Magnus wouldn't have dreamed of hugging the captain, and by the time they got closer everyone knew him well enough to know it's not his thing. He shows his affection in other ways: warm words, a clap on the shoulder, a gentle order to get some rest.
The first time Magnus sees Davenport after the final battle, he goes to hug him as he has hugged all his family on their reunions. Then he remembers, and stops, and holds out his hand for a handshake instead. It's Davenport who pulls Magnus in for a hug, just this once, because after everything they've been through, he knows that Magnus needs it.