I've always been intrigued by the D&D paladin class.
Due its strict code of conduct, it has always been one of the hardest class to role, expecially in older editions.
For this reason, I think, at my tables very few players choose it.
With the 5th edition, to be a paladin is much simpler, but to stay adherent to the chosen Oath requires good role-playing skills and some difficult choices.
There you find some quests for specific events in a paladin's life: to retrieve a relic (or a Holy Avenger sword) or for atone for some sins.
To retrieve relics or a Holy Avenger
1) The relic is warded by a Guardian Naga in a cave inside a vulcano. In order to grab it the paladin must challenge a red dragon and some fire mephits that now lives there.
2) A Holy Avenger sword lies at the bottom of a swamp with the corpse of the last paladin who wielded it. The paladin must defeat the will o' wisp that rules there and find a way to retrieve the sword.
3) A relic was lost at sea many years ago after a huge storm. The paladin must reach a sunk ship that now it's a lair of many sea monsters such as sea trolls, sea hags and a Kraken.
4) A Holy Avenger sword is stuck up to the hilt between the scales of a gargantuan reptilian on a island far away from the continent.
5) A relic is used as part of a magical engine which animates a construct, such as a golem or a shield guardian, which was created by a mad wizard. It's inside the construct.
6) A Holy Avenger sword is in a silver dragon's lair. She was at the service of the dead paladin who once owned it. The paladin must prove to be worthy to receive the sword by passing the tests which will be assigned by the dragon.
1) The paladin must build a shrine in a border town in a semi-civilized area plagued by continuous raids of humanoids tribes.
2) The paladin must reach an isolated village on the top of a mountain. He must cure a little girl who's dying of disease. On his journey he will face bandits, wild beasts and natural hazards. The girl is going to become a great priestess of the paladin's deity.
3) All the world is paralyzed as if it's under the effect of a huge time stop spell. The paladin however can freely move and act. He must find and kill a nemesis of his who is his perfect copy and can freely move too. If he manages to kill the nemesis, time will start to flow again normally and he will be brought back to his right time and place but if he fails time will start to flow again normally and he will disappear and nobody will remember about him.
4) The paladin must donate all his money and any other things of value to poors or to his church. He'll have to live as a beggar for 1 month, counting only on charity from others (not from other PCs!) to gain money and food, and he will learn the true meanings of humility and respect for the weakest.
5) The paladin is sent to the royal palace to become the tutor of the Crown Prince, who's a rude and lazy boy. The paladin will have to correct the prince's flaws without get angry the king, who madly loves his son, and he will get involved in many court plots and treasons.
6) Two tribes of humanoids are at war and their conflict is damaging the nearby human-controlled areas. The paladin is sent as an envoy to sign a peace treaty between them.
Those are only a few of the many possible hooks that may give you numberless adventures and plots for your campaigns.