When looking things up in Japanese, to this day I still have to run "Kana System: Take Note How Much You Read and Write to remember the order.
In high school German, our teacher taught us Weuf Dog (wieder um entlang fur durch ohne gegen) to remember the accusative prepositions.
For the dative:
aus-ausser-bei!
mitt-nach-zeit!
von-zu-gegenuber!
Aaand then there’s the obnoxious “Fifty Nifty” song that allows me, some 30-odd years on, to still remember the US states in alphabetical order.
That’s Chief Soh Cah Toa to you people. Honestly.
From chemistry, I remember that LEO goes GER. Lose electron = oxidation, gain electron = reduction.
There’s something similar for physics that (I think) involves ICE, but I can’t remember it anymore. Apparently it wasn’t very effective.
My husband took a course to be in the ski patrol back in college, and to remember which bone of the lower leg is located to the front of the body, the instructor told them “Tits go in front.” He didn’t have a better way to remember that it’s the tibia that’s in front, but he guaranteed them they’d never forget it after. And he hasn’t.
In high school, I learned the quadratic formula to the tune of “Pop Goes the Weasel.” Now, if I ever need to use it, guess what tune I have to hum?
For Latin:
P-PAIN words (pirata, poeta, agricola, incola, nauta) for first declension nouns that take masculine (-us) adjectives.
Great, 'cause they work forward and backward.
I learned:
Sharps: Fat Charlie Gets Donuts After Eatin’ Breakfast
Flats: Breakfast Eaten After Donuts Gets Charlie Fat
I think Big Bird uses that one, too.
Can I have a large container of coffee.
How I like a drink, alcoholic of course, after all these chapters involving Quantum Mechanics.
All Altruists Gladly Make Gum in Gallon Tanks is the mnemonic for the hexoses in binary order if you look at the Fisher projection. It always annoyed me, because I’ve known it for twenty years but had to look it up every time I wanted to tell someone else about it. It’s not a very memorable mnemonic to me.
For me, it’s more like:
A, B, C, D, E, F, G
H, I, J, K, LMNOP. . . .
Those last few always get run together whenever I have to look things up in an actual, alphabetically arranged book.
To remember the Papez circuit in neuroscience, I pictured Napoleon (why??? no idea) and remembered:
He Fought Many Men And Ate Caviar In Paris
Hippocampus, Fimbria-fornix, Mamillary bodies, Mamillothalamic tract, Anterior Thalamic gyrus, Anterior cingulate gyrus, Cingulum, Isthmus, Parahippocampal gyrus.
Lots of medical school (especially anatomy) relies on mnemonics - I bet you could ask almost any doctor to complete the sentence, “As Sally lay flat…” and get the remainder of the old mnemonic -
For the branches of the external carotid artery:
As Sally Lay Flat, Oscar’s Penis Slipped Medially
Ascending Pharyngeal, Superior Thyroid, Lingual, Facial, Occipital, Posterior auricular, Superior Temporal, Maxillary
Cranial nerve function?
Some Say Marry Money, But My Brother Says Big Boobs Matter More
(Sensory, Motor, Both)
Can’t you simply alphabetize them, left-to-right (B, then D)?
I may look a little less silly at the dinner table. 
mmm
Aha! I remembered! It’s “ELI the ICEman” for physics: voltage leading current v. current leading voltage in different circuits. (I did have to look up the application - I vaguely remembered “something leading current” but couldn’t come up with what. I’m no great shakes at circuits.)
Elephants And Dogs Grow Big Ears for guitar strings.
SEX - Statement , Explanation, eXample - Structure of an essay paragraph
Hehe Libeebkinoffnee - The First 20 elements of the periodic table
(H He Li Be B C N O F Ne)
My dad, a chemistry teacher, had the first 100 or so memorised - It sounded like he was making a speech in indonesian or something!
A funny mnemonic that is fairly new is “Oh Boy A Feral Giraffe Killed My Little Transparent Yeti”. This mnemonic refers to the classification of stars in astronomy. it stands for OBAFGKMLTY. Yeah that’s a lot of random letters that you need to remember in exact order.
Each letter stands for a certain classification O being for the hottest and brightest stars and Y being for the dimmer stars. This is a newer mnemonic because the letters LTY were just added less than 5 years ago for stars we call brown dwarfs. These are stars that are like really big planets but at the same time really small stars and they are super dim. In some cases you could be right over one and you wouldn’t see it. I saw the mnemonic in a crash course I was watching on YouTube and I haven’t seen it anywhere else.
DePP NuDGe – Dead car’s Positive to Positive; Negative to Dead car’s Ground
To know the correct (ascending) order of the general officer ranks: Be My Little General. That’s for Brigadier General, Major General, Lieutenant General, General. Yes, that’s how the Drill Sergeant taught it to my platoon in BCT.
King Philip could often fuck girls senseless. (Kingdom, phylum, class, order, family, genus, species)
For me it was always King Peter could only fuck golden sheep.
‘My Friend Jimmy Is an Opportunistic Sexual Predator’. (I use that one to remember why I don’t trust my friend Jimmy.)
I was taught that the right hand is the one with the thumb on the left.