Mugen
Of the three, Mugen is possibly the most mysterious. The only thing we know about his past is that he's from Okinawa. Everything else, where he learned to fight, why he's in Japan, etc, is a total mystery.

At first, Mugen despised Jin and the feeling was more or less mutual. After several duels in which neither is able to get the upperhand on the other, they eventually settle into a grudging stalemate at Fuu's behest and, soon, develop a sort of respect for each other. Alll things considered, Jin is the closest thing Mugen has to a friend and vice versa.

Mugen is Jin's equal in combat, although his style in the polar opposite. His style of swordfighting is heavily influenced by breakdancing (...) and he's just as likely to flip around and smash his sandals into his opponent's face as he is to gut him.

Finally, Mugen is quite a drinker and womanizer, although women usually come on to him (though, to be fair, they're often assassins in disguise.)