"Sex. Muscles. Humor. Thuggery. Jayne."
-- Adam Baldwin, summarizing his character
Jayne Cobb - The Mercenary (played by Adam Baldwin)
A mercenary who didn't fight for either side in the Unification War, Jayne works for whoever pays him the best. At the moment, that's Mal, so that's where Jayne's loyalty lies — until something better comes along.
But Jayne also has an unexplained loyalty specifically to Mal indicated by an unwillingness to betray the Captain even when the terms are very good (Serenity Pilot/Agent Dobson). He jokes about it later with Mal but it is apparent that going against each other is also a prospect neither of them look forward to, which also indicates Mal might also be the only person Jayne is actually a little afraid of. It is possible Mal saved his life at one time or the other as Jayne is not given to close relationships. But he does treat some of the serenity crew with a surprising amount of closeness, almost bordering on family.
He also makes sure not to betray Mal on Ariel along with River and Simon, though he did not seem to realize that the Captain would take the betrayal of one of his crew equally personally. Also note that the Captain opts to surprise Jayne, knocking him out with a wrench after the Ariel incident, rather than confront him barehanded or with a gun.
It is implied a couple of times that Jayne is not just physically the most dangerous, but also the best shot of the group. First when he tells the Preacher about taking a head shot at 500 yards with a broken scope and second when Kaylee describes River's shooting style and says even Jayne wasn't that good (but River's abilities being out of control and unreliable).
Jayne stores his guns just above his bed — appropriate since his favorite posession is a gun he calls Vera (Our Mrs Reynolds). He's a tough fighter who can take a bullet or two without much complaint, and an expert marksman. For all the talent Jayne has for combat, he's lacking in social graces, which frustates Malcolm Reynolds on more than one occasion.
It is also implied a couple of times that Jayne is an expert tracker. First in the Pilot where Mal sends him to track and take out the snipers and second, when Jayne is introduced to Mal and Zoe in out of gas and Mal inquires who actually tracked them and makes Jayne a better offer to join them instead.
But there's more to Jayne than meets the eye; he also shows a human side:
He is almost always touching or smelling something. This becomes more pronounced as the series continues and is quite pronounced in Serenity.