I help host a speedrun show so I've seen a TON of jump mechanics in old platformers. Figured simpler is better so I went with NES games, excusing some of the examples already posted.
Banana Prince - You can press down and jump to plant a beanstalk and then do a big spinning jump off of it
Batman - Winds up to jump, limited air control, very slow terminal velocity, not to mention the wall jumps (also with a wind up)
Blaster Master - The floatiest tank
The Bugs Bunny Birthday Blowout - Very odd movement in this game, seems to run at 30 fps, very slow terminal velocity
Chip 'N Dale Rescue Rangers - Your vertical speed immediately stops the frame you let off the jump button, feels very tight
Conquest of the Crystal Palace - Tall jumps with limited horizontal speed, attacking in mid air immediately causes you to start falling, can call in a dog and jump off of him (the dog is fucking cool)
Contra - Floaty jump, very slow horizontal movement, can change direction in mid air but you cannot stop horizontally until you land
Darkwing Duck - Lots of control over your jump height, very sleight pause when jumping/landing that can be avoided with another well timed jump (watch the Tool-Assisted Speedrun avoid the pauses by never stopping jumping)
Dr. Chaos - This jump is all kinds of fucked up I can't even really put my finger on it, especially when you contact enemies
Kabuki Quantum Fighter - 2 jump heights, tap down to interrupt jump and start falling, cannot move horizontally while down is held (can hold down and mash A to freak out)
Kick Master - High jumps, gets more interesting when you level up and unlock new kicks
Krion Conquest - Glitchy. Jump off a platform, pause the game when you're below the platform, hold A and unpause to rejump. Can summon a broom to walk on but if you don't jump way on top of it, it disappears and you fall. Holding select locks your position in a truly bizarre way.
Kung Fu - Committed jumps, don't stop horizontally but you have a weird wind up on your vertical height. Can't actually punch or kick until well into the jump.
Legacy of the Wizard - 5 playable characters with different speeds and jump heights. Parts of the labyrinth are gated by jump heights. Has a similar pause-to-rejump glitch like Krion Conquest. Very big bounce falling from a great height, halts horizontal movement while it happens.
Mighty Bomb Jack - Super high jumps with the ability to float very slowly give you tons of aerial control
Mr. Gimmick - Has a star projectile that bounces off walls which you can ride on. The arc of the star is dependent on how you're moving when you release it. Can preserve increased speed from going down an incline by repeatedly jumping.
Ninja Gaiden - One jump height, limited air control, can attack fast enough to hit ground-level enemies right out of a jump, as well as when landing. Spinslash powerup turns your jump attacks into an invincible spinning ball of death that deals damage every other frame. Climb walls by sticking to them, jumping off and regrabbing.
Panic Restaurant - ..................................I just like the animation, honestly.
Rockin' Kats - Standard jump but you have a punch glove that can propel you off of surfaces (really weird in vertical stages), or grapple onto things and launch yourself at 8 different angles (including backwards).
Rygar - Floaty jumps, awkward jump hitbox, can jump off of enemies to stun them temporarily.
Shadow of the Ninja - Fast jumps, attacking in mid air lurches you forward awkwardly.
The Simpsons: Bart vs. the Space Mutants - Jump button is also the run button and you accelerate in mid-air. Big awkward jumps.
Strider - The world's most awkward wall jumps (you have to hit the button soooo late!).
Super Mario Bros. - Obvious. But seriously, play around with his jumps. You can't accelerate in mid-air so you can get locked into some very slow jumps, you instantly fall if you grab a mushroom, you can land on top of an enemy even if he's above you as long as you're technically on the 'moving down' part of your jump, and jumping backwards has a weird acceleration to it.
Teenage Mutant Ninja Turtles - 3 different jump heights, including a very very tall jump, especially since you move forward so slowly. Awkward hitboxes mid jump.
Tiny Toon Adventures - Sliding is faster than running, and if you jump out of a slide you can preserve that increased speed. The catch is you have to release right and the run button, so the fastest method of travel is a down-A input. Plucky's hover ability also preserves that speed and you get tons of height bouncing on enemies, letting you soar across levels.
Wizards and Warriors - Big floaty jumps for a guy in full plate. Slight wind up on take off and landing. Sword hitbox is active while jumping!
Some of these you probably get the jist of simply by reading the description, some you'll want a video for, but there's a couple you'll want to download a ROM and mess around with like Mario, Strider, TMNT, and Rockin' Kats. Hope this helps!
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