I've always wanted a "physical transformation/body horror" Barbarian archetype.
Two for Bards I can think of are a College of Dirges (necromancy focused) and College of Hymns (psuedo Cleric basically). I've seen both in homebrew (even made one of them myself), but having official stuff is always nice.
A Chaos-esque domain for Clerics has been mentioned, and one that I would like (I think Order fits for Law, and maybe Trickery works for Chaos, but it's a loose fit.) Another domain I'd like to see is Travel, but that's more personal preference then anything.
This is more gameplay than story, but a dedicated Blaster Druid would be nice to have.
A Throwing based Paladin would be neat, just don't really know how you would tie that to an oath.
I would like an Undead sorcerous origin, maybe have it leech life and turn it into sorcerer points?
Noble Genie Warlock is one that I am honestly surprised hasn't even been mentioned by WotC.
For a new class, I'm always gonna want a Summoner like in Pathfinder, though that might just be because I'm a big fan of Persona and want some of that in D&D.
One kinda unrelated but I want is a Fighting Style for using Versatile weapons with two hands.
That's what I can think of now.