The halfling cleric I detailed above was the result of randomly rolling stats, race, background, personality traits, ideal, bond, flaw, and a trinket from the table at the end of the equipment chapter and then creating a narrative that fit them all together.
Here's a sampling of some less conventional characters from the same kind of random rolling:
A wood elf barbarian acolyte who feels his faith must be upheld at all costs, worships a hero of his faith, seeks to protect an ancient text that other sees as heretical, and is very inflexible in his thinking. This sounds to me like fanatical cultist, so I made him a member of a band of outcast wild elves who worship Fenmarel Mestarin, the elven god of outcasts and wild elves. Incidentally Fenmarel is called the "Lone Wolf" so he's already lined up to become a totem warrior taking the wolf as his totem. For his tribe, he's a holy warrior, and his rage is a divine blessing.
A tiefling barbarian sailor who works hard, plays hard, swears like... well, a sailor, tends to be view respect among the crew and commitment to the ship as more important than personal bonds, and won't back down form a challenge. I decided to opt for the pirate version of the sailor background to create a former pirate trying to get out of the underworld. But he's got a bad temper and a chip on his shoulder.
A human bard entertainer who is unreliable to his friends, but hard to stay mad at. He likes to tell stories and is prone to bold action. Someone stole his prized musical instrument and he hope to get it back. I wanted to put this character on the path to the College of Valor, so I took the gladiator alternative to the entertainer background and pumped up his strength a little. So he puts own show fights where he wields an ornately decorated greatclub, blasts a warhorn (a replacement for his lost prize), regails the audience with tales of his deeds and compares himself to legendary heroes, and then buys his opponents a drink when its over. I see this guy as sort of a D&D version of an over the top, ostentatious WWE star that looks like the bare-knuckle boxer dude in the hyper-masculine man memes.
A dragonborn fighter urchin who prefers to stay unseen, unnoticed, and is wary of false kindness. He wants a better life and will do most anything he can to earn some gold to get there. The funny thing was I rolled the personality trait for urchins that say "I like to squeeze into small spaces" and then rolled a random height of 6' 7" and wt of 279 lbs. So I picture this huge, hulking dragonborn trying to squeeze himself as tightly into the corner of a tavern as he can because he's nervous in crowds. Funny image. Anyway, I made this guy an orphan whose clan died near a human city and he wound up living on the streets there. He doesn't even remember his given name, just his childhood knickname "Shieldbiter" so he goes by "Biter".
A dwarf monk entertainer. I randomly rolled his type of performance and got fire-eater. He strives for perfection, believes art should reflect the soul, is a sucker for a pretty face, is very loyal to his troupe, and has a story for every occasion. So I made this guy have a very fiery temperament as a youth. He was supposed to become the clan's lorekeeper and historian, but he was just too rowdy to study. His parents sent him to a monastery to learn self control. I decided to put him in line for the Four Elements path and that he learned fire-swallowing as part of disciplining himself. With no real place for him back with his clan, he decided to travel the world and continue his path of self-development. He fell in with a group of traveling entertainers and performs monk-like feats of physical discipline and is the fire-eater. He has flame tattoos all over him. (Maybe he and the bard are buddies).
A human sorcerer (blue dragon heritage) outlander. He has a love of the wilderness, an innate curiosity about things, a thirst for glory and a preference for solving problems with violence. Sounds a bit like Conan to me, except he's a scrawny sorcerer. And I also rolled that he was, in fact, raised by wolves. So I pictured this guy has being found by a nomadic pack of longtooth shifters and raised among them ("raised by wolves"), but he was always the runt and developed a bit of a small man complex. But at puberty his sorcererous heritage started to manifest so now he likes to pick fights with big guys and zap them with his spells.
A human cleric folk hero who once robbed a corrupt merchant, values honesty, likes to inspire confidence in others, never gives up, but has a but has a love for hard drink. For this character, I determined that he was a simple farm boy who grew tired of local corruption. Being a big strapping lad, one night he but on a homemade mask, robbed a crooked merchant and left he tied up and bruised in the town squire. Everyone figured it was him and the local priest took him in to the temple and had him take vows before he could be arrested, providing him sanctuary. But everyone was more willing afterward to begin standing up for themselves. Now as a full-fledged cleric, he protects the common people from oppression and spreads the message of fairness and justice for his deity.