Anyone have any monastic orders you put in your game?
I haven't yet, but I have a player who is playing the first monk (mystic) in my bespoke D&D for ~8 years, with only three in the past 20. I have some issues with the class mechanically, but, weirdly, I haven't come up with different orders yet. I'll have to get on that.
My temples, magical orders, fighting guilds, druid circles, &c., are many, but haven't given much thought to monks yet.
Mechanically, I make take some inspiration from a few third party interpretations of the monk.
Arcana Unearthed had the
Oathsworn, inspired by the Bloodguard from the Thomas Covenant stories.
Midnight had the
Brawler, quite handy when weapons are forbidden. ACKS has the
Mystic, inspired by the Bene Gesseret from
Dune. Plus there's what inspiration you can glean from Avatar; I think element bending is a great theming element (heh). I do appreciate 5e's use of "focus" as a defining mechanic. Might use that to refine my class, although I might call it "vril".
I would argue Paladin comes up as often as cleric -- if you hear someone say "cleric" in conversation, chances are they're talking D&D.

Actually, a friend of mine is an Episcopal priest. She refers to herself as a "cleric" all the time.
She
does not refer to herself as a "priestess", however. That gets you the frown of judgement.