My game is Broken Robot, which is a puzzle platformer where you can only press each direction one time per stage. I used the only one in multiple places, but I found that limiting going left, right and jumping to only once per stage really made me think about what I was doing more than most platformers. 

https://itch.io/jam/gmtk-2019/rate/462219

https://kdharrington.itch.io/terry-flight

I have used only the mouse as the "only one" control.

Link:

https://itch.io/jam/gmtk-2019/rate/461991

Mine is only using the left mouse button, for shooting and moving, (and I planned to do it for switching weapons as well, but I didn't have enough time to finish it, so I cut that part out, but I might reimplement it after the voting is over).

Check it here: https://itch.io/jam/gmtk-2019/rate/462640

No Exit: https://itch.io/jam/gmtk-2019/rate/431948

One button fast paced plat-former, one direction, one sprite, one background, addictive swing mechanics,  cool graphics and  sick beats and rage enduing feature.   

Smooth elevator has only one control: any key

Hey I think my project qualifies for that.

You go right, left and also teleport left or right with just space.

If you wanna check it out :p https://nulmor.itch.io/ruuun

Apart from displaying only one full-screen color at a time, One Color Dungeons is also one-button: you navigate the game and fade the color that telegraph what's happening by pressing and releasing Space.
https://itch.io/jam/gmtk-2019/rate/462105

in this game grandma can only run OR attack! also, she needs a while to get going, but builds momentum!

https://itch.io/jam/gmtk-2019/rate/462916 

I went for the only one being controls too. I decided on a system of taps vs holds to control a character in an infinite runner style game. Check it out if you want at https://itch.io/jam/gmtk-2019/rate/461415 -- I ran out of time for creating a better difficulty curve, so right now the game is a little punishing, but if you like games with a learning curve, I'm finding it pretty addictive!

Yeah, my game uses only one button to go forward (and not pressing it to go backward). A flappybird kinda input.

https://elendow.itch.io/martian-scout

Same here, one button tap and hold combos controll the whole game: https://sleeper-games.itch.io/mech-revenant-input-one

Vapornouts did a nice take on the one button controls, since you have to controll your cursor on the UI on top of that and actions need different kinds of inputs to be executed or turned off again: https://jamjamteam.itch.io/vapornaut

My game The Only One uses only the mouse to control which means you can use only walking.

https://itch.io/jam/gmtk-2019/rate/463844

Nice one! In mine, the only thing you can do is clicking to swing your sword, and that is the only way you can move, attack and defend yourself. You can play directly in your browser : https://itch.io/jam/gmtk-2019/rate/462432

The restiction really made for some intersting gameplay.

Cheers!

Only one button. 

You can play it here:

https://itch.io/jam/gmtk-2019/rate/463337

Hi! Our game also includes a limitation in the controls...

It is a fishing game! You control the bait with only one button. Yeah, it is kind of basic, but the "only one" is also included in the game in other ways: you want only a certain fish... and it appears only one time!

Please take a look :)

https://buendiagames.itch.io/the-only-man-and-the-sea

The only control for my game is clicking the mouse. It's not the main "Only One" design choice that I was focusing on but definitely part of the experience. It's kind of an endless runner where, after a short intro/"tutorial" bit, the screen fades to black and you're left with only sound to guide you. I felt like anything more complicated than a one button control scheme would have detracted from the only one sense thing I was trying to do.

Blind as a Bat

(Also its browser playable)