This seems weird question I know :p. Since transmog feature all my banks are empty. Materials go to reagent bank. Toys and heirlooms now are in collection tab as well!
All my characters banks are empty and I wonder, how is yours? What do you keep in there? Trying to get some ideas, maybe there are fun stuff I missed 
I keep old things like this:
And this:
Legendaries, keepsakes, mémoires and artifacts are all I have really.
But it fills most of my slots.
Crafting material both from this and other expansions, gear I don’t want to vendor that meant something in the past, items that can give reputation and since I want my bags more clean I put in things I don’t need right now.
On low level bank characters I keep green gear for alts and mats that is to overwhelming to have in my main bank.
Special Tabards like Tabard of Brilliance, Flame, Void ect
Items like Garrison resource caches
Legendary Weapons and Legion Weapons
Certain event items that I don’t want to have to rebuy when the event comes round again.
Items that should be toys but still are not, like the teleportation item that sends you to random places, no idea why it is not a toy yet.
Certain books and letters, that are unique and can’t be put in void storage
And other misc items that I hold onto because they do something cool, are removed (unobtainable) from game or I don’t want to get rid of incase it is ever needed
Stuff from earlier expansions. Even my void storage is full.
Materials for professions I promise I will level…
More useful stuff like item fragments and quest items languish in my bag.
Tabards mainly.
Also stuff you can no longer get. I have all the leaflets from the cata? pre event.
Barely anything, some crafting mats on one char, rest of my characters have never even been to the bank.
craft matrials and world event tokes and other stuff.
I use the bank to hold my collection of Fishing Rods.
Brewfest mug, legion oranges, artifacts and free shirt day shirts.
I’m my back I have all the crap I have accrued on my char, oldest item in there is my thousand needles boat, and then also legion troop tokens.
100 original brewfest rams because it looks good
My legion artifacts and salacious dresses of course
lots of food, crafting stuff, gems, jewelcrafting stuff, tailoring stuff, etc.
As for fun stuff, a bunch of duplicate mounts, legendaries, some toy items that aren’t actually toys, some source removed from game items and some lore related pieces like voljin’s ashes.
i hoard all manner of old items i used to wear in previous expansions for the memories. unfortunately my bank is completely full, so i don’t really know what to do now. i don’t want to stick them in the void storage and lose the enchants and gems.
Haunted memento. Still got stuff from TBC like the steam toy from quest reward ect lol
I still have my dartol’s rod of transformation and some items that were removed in cataclysm.
On Souldefiler all her legendaries (including legion and prior) my light bringers tabard.
Only other toon with a bank item I would never let go is Soulclaimer and her Nerubian quiver
Crap I think I might need but never do.