I'm designing a Kensei monk that comes from a clan of dungeon delvers and weapon collectors. Their group basically aims to find powerful weapons and archive them, and it is each individual's responsibility to collect as many artifacts as possible... Except, my monk thought that his clan's ways were too "old fashioned"; he decided it'd be easier and quicker to challenge powerful individuals and take their items if they lost to him, and eventually sort of became a glorified bandit.  

In a recent Adventures League game someone mentioned how rare the sailor and pirate backgrounds were used and I thought about how perfect pirate is for Kensei monk.

You were first mate on an infamous pirate ship and were known as the most dangerous fighter on the crew, equally comfortable on land, on the deck, or on the masts and rigging. Armor restricts movement while swimming so you went without. You took up the longbow to pick off officers on the target ship before leaping into the fight, sword in hand. Just be sure to snag a proficiency in intimidation and a charisma bonus to make the most of your fearsome reputation.

Quote from Z0mb13_Phrog >>

In a recent Adventures League game someone mentioned how rare the sailor and pirate backgrounds were used and I thought about how perfect pirate is for Kensei monk.

You were first mate on an infamous pirate ship and were known as the most dangerous fighter on the crew, equally comfortable on land, on the deck, or on the masts and rigging. Armor restricts movement while swimming so you went without. You took up the longbow to pick off officers on the target ship before leaping into the fight, sword in hand. Just be sure to snag a proficiency in intimidation and a charisma bonus to make the most of your fearsome reputation.

 it's possibly because sea faring isn't common and not many like it as far as i heard. Kensei monk with possibly a scimitar and a pistol as a range weapons does sound very tempting....

I have two monk ideas:

First (and somewhat cliche) - a scribe from the local monastery / archives. At first level he's sent out to take a letter from the HMFIC to somewhere distant. He winds up traveling with some odd group and goes through Some Stuff he wasn't prepared for. He takes to drinking to cope and eventually discovers the Way of the Drunken Master.

Second (with a hat tip to Terry Pratchett) - a janitor whose kensei weapon is a broom (reskinned quarterstaff). At some point he'll need to branch into a homebrewed Way of Deja Fu.

I ran a Lizardfolk Kensai monk.  He would slash, bite, kick and tail slap opponents, while his eggbrother (An ancestral guardian Barbarian) kept all the focus on him.

The pair's backstory were that they were investigating local human cities to attempt to understand how a weak species seemed to be spreading everywhere.  We got hired as muscle to help a party with a problem with an ogre (aka, we replaced a player that dropped out) and ran with the group as partners for almost 2 years.

Considering our inability to understand idioms, solving all problems in the quickest most violent way possible, and generally straightmen to the other party members wild schemes and antics, it was amazing we were able to save the world, with most of the silly softskins in them.  Still might have been a mistake. 

Currently playing an insanely fat halfling monk who has unnatural control over his own weight. Beats people up with his flab rolls.

I played as a monk with the criminal background.

I plan to play a Simic Hybrid, Way of the Open Hand. All the monk features would be reflavoured as my character's techniques and mutations

My guy is a wandering detective in Exandria who is more of a cowboy then a monk.

A fight club... Underground anarchist faction. Members ingest a special drug compound made from demon tainted plants. This allows them to tap into special abilities. 

Librarian (Sage Background)

Subclass: Way of Shadow

You took your job VERY seriously…when someone raised their voice in Candlekeep; you were there to inflict “Silence” on them, drop in, “Stunning Strike” them, and toss their ass back out on the street.

And if someone was late to return their book; you hunted them down in darkness, bonked them, and reclaimed the book.

…needless to say, there were some complaints.

Fired from your job, you now try your hand at adventuring; but the occasional loud, disruptive sound of drunken braggarts still causes your knuckles to twitch with irritation.

Shadow Monk abilities are a manifestation of my dhampir's curse. Her background is "haunted one" due to her early years as a vampiric predator.

I created this backstory for my half-orc Monk Gromak Stormstrike, based on his race and the last name a generator gave me:

An orphan due to his heritage, he was saved by a half-ing monk and brought to the Stormstrike monastery high in the Greypeaks at the age of 3.
The monastery specializes in giving half-race orphans a home, then training them in study & fighting.

He’s currently on his “rumspringa” for three years to get more half-race orphans; this journey starts at different ages determined by his Prior.
He started later than normal - at 25 (most start b/w 20-22), due to his Prior being cautious about his ancestry, making sure he had mastered his internal chaos.

Being from an monastery (all male) is awkward/aloof around women. Additionally, he is weary - and slightly judgy, about wealth & intoxicants, and other "low, worldly activities" like gambling.
During his travels, he begs with his alms box so that he may at least get money for local orphanages.
[this last point has me asking the DM if I can get a orphan to train, sorta like a squire for a Paladin]

I use official background that's in the Player's handbook at the same time I select the species

I like the idea of someone who grew up in a peaceful idyllic natural setting, like a small village of wood elves or maybe halflings in a remote forest. The character spent their youth climbing trees, running through windswept fields, swimming in rivers, listening to the rain, and observing all the various animals around them. Of course children like to imitate what they see, so the character grew up imitating those animals, trying to connect with them both in form and temperament. Eventually this developed into a sort of mystical connection between the character and the natural world around them, which presents itself as amazing physical and mental abilities. So the result would be a Monk, Way of Mercy or maybe Way of the Open Hand. As for background, Guide is perfect. If gives bonuses to Dexterity and Wisdom, and it gives you a couple druid spells to start with, thanks to the Magic Initiate feat.