Looking for fun/innovative games like Octodad or Jazzpunk

Totally accurate battlegrounds. You might like it, but it's multiplayer, and I don't know how many people are playing it.

Human: Fall Flat or Gang Beasts, maybe?

If you like games that make you struggle to control them, there's Manual Samuel and Snake pass.

Maybe try something from here or here or here.
With Event[0] featured in a video of its own.
With games with unique movement, Grow Home was liked too.

Absolute Drift
Gunpoint
Rock of Ages 1 & 2
SUPERHOT SUPERHOT SUPERHOT

Hue, Braid, Crawl, Epistory, Her Story, Superhot, Contrast, Elegy for a dead world, Kwaan, One finger death punch, OneShot (just trust me and don't read anything about it), The Sexy Brutale, Why am I dead at sea.

Pony Island ?
Turbo Dismount ?
De Blob and it's sequel probably.

On, and not new, but a remake that should appear on PC in December: Katamari Reroll. na naaah nananah nanah nanah na naah na naah na nah naaah!

I Am Bread?

The Howler

Don't see it mentioned, but 'Stick it to the man' is also quite 'quirky' and funny.

Try Pony Island and Gorogoa! In general, I'd recommend checking out the Nuovo Award finalists and winners from the IGF, which is designed specifically to commemorate games with innovative gameplay.

Out of the more popular games a lot of great stuff has already been mentioned :)

I'll add a few more rather well-known bundled titles:
Goat Simulator
Surgeon Simulator
Brothers - A Tale of Two Sons
Snakebird

And here are some newer/less-known innovative games I look forward to playing. All of these are from my wishlist and most of them are unbundled:
Donut County
Semblance
Baba Is You
Dude, Stop
All You Can Eat
FAR: Lone Sails
Light Fall
OCTAHEDRON
Minit
Octogeddon
Pyre
Recursed
Circa Infinity
A Good Snowman Is Hard To Build
Chariot

Recently I gave Mushroom 11 a shot and it's quite a unique game with very innovative controls. Quirky and intuitive, yet not very easy.