I've been reading the new Dragonlance today, so that's on my mind right now and all this assumes a Dragonlance game.
Artificer - human alchemist. An arrogant genius jerk who ain't waiting for the gods to come back, and is confident that SCIENCE can fill the healing magic gap. Doesn't talk about a bit of a history of graverobbing and possibly a vengeful freewilled flesh golem in his past...
Barbarian - reborn storm herald (tundra). Partial amnesiac, who was pulled unbreathing out of a frozen river with a dagger in his back by a passing Solamnic knight and never ... quite ... recovered. Became a squire, since his only memories are flashes of him being a thug burning down houses and laughing at weeping terrified innocents, and he doesn't want to go back to being that guy. Heart beats only a handful of times per hour, body temp is continually almost at freezing point, his archetype abilities (and feral rage when he fights) reflect his quasi-undead status.
Bard - human college of valor. Middle-aged Solamnic knight who got soft when his wife (also a knight) died on a mission and he had to retire from active duty to raise their daughter. His old armour doesn't fit his belly any more, and he's more interested in diplomatic lunches and entertainment and reciting the old glorious tales than he does about actually demonstrating honor and undertaking quests these days. He calls it important work but the other knights sneer a bit.
Cleric - forge domain (i hate the archetype's Channel Divinity feature, but nothing's perfect), elf. An anomalous and social-skill-deprived elf worshipper of Reorx with ambitions of being the one who forges the next legendary weapons of the elves.
Druid - circle of the land (grassland). Plainswoman whose druidic powers sprung up out of nowhere one day, and whose was 'encouraged' to move far away by her tribe who thought she'd been dealing with dangerous fey for power.
Fighter - human battlemaster. Tiny adopted daughter of a Solamnic knight, Dex fighter who was never going to be big enough to wield the ancestral greatsword so had to learn tricks instead. Her impulsive, bad-tempered elder (non-adopted) brother took the sword but has left the knighthood and rumours whisper he's now a sellsword or even in the dragonarmies. Not yet aware that her adoptive father killed her real mother (who was a crime lord and assassin) and raised the orphan as his own.
Monk - Ascendant Dragon. Gully dwarf, from a small and little-known monastic tradition among the gully dwarves that reveres and remembers dragons, but whose oral tradition has meandered very far from reality over the centuries and almost everything they believe about dragons is wrong.
Paladin - theiwar (duergar) oath of vengeance paladin. Was a cold and clannish murderer in service of his corrupted thane, but a mission outside thorbardin opened his eyes to the wider world and now he wonders whether he's taking revenge on the right people, or whether there's those out there who are more deeply, funamentally responsible for the plight of the dwarves that he should be focusing on instead. May multiclass into assassin rogue.
Ranger - kender beastmaster using the updated Tasha's rules. Beast companion is a giant ant, and if/when it dies, a replacement digs up from the ant tunnels beneath the ground almost instantly. Yes, this is creepy for normal people, but it doesn't bother him. Rather than curious about other people's possessions, is curious about the natural world and insects and will tell you all about them even if you beg him to stop. Hoopak doubles as a butterfly net.
Rogue - gnome swashbuckler. His family life quest is to investigate the most efficient methods of loading and stowing barrels. Went to sea to do first-hand research on this, but had far too much fun fighting pirates and venturing to faraway places and gambling and partying. Now secretly thinks barrels are boring and hasn't done any research on them for ages. Deeply loves his family and is dreading them finding out about how he's disgracing himself.
Sorcerer. Lunar. Daughter of the bard above, raised on stories of Solamnic heroism and knighthood. Idealist, wants to fight for the cause of Good, gets herself in trouble.
Warlock. Half-elf undead pact. Her 'patron' is the embittered ghost of her elven grandmother who loathes her and the disgrace she brought on the family by existing and who is bound to haunt her in death. They share a body, and the levelling up process for her is each of them trying to control and master the other.
Wizard. Illusionist. Travelling painter who specialises in court portraits etc for nobles. Knows a few spells to help her out in her trade, but never took magic more seriously that as something fun and pretty. Will probably soon be forced to change her attitudes in that department.