You might want a cheese grater patch bay:

They're easy to make yourself from about 20 jacks, a soldering iron, and spare wire. You'll still have to plug things, but it will be from the front.

not sure what you mean by "pro studio rack" but a distinctly un-pro small mixer shouldn't set you back more than £40 (60USD??) and you'd get the added flexabilty that a mixer gives you.

Any of the home entertainment or video game related "Audio/Video switch box" type devices will do just what you're looking for.  Just ignore the video plug and get some 1/8" to RCA adapters and you're golden.

Example:  http://www.amazon.com/3-Port-Audio-Vide … lector+box

edit: damnit yogi beat me to it

I use a simple 4-to-1  A/V switch box, no amps or auto switching, just simple mech 'radio' push buttons. The type with RCA plugs for composite video. Each switch input can handle 3 signals, so if you aren't using video you could ran another audio channel through the 3rd one. I run my stuff into a regular stereo and a TV, so works for me. If you added a second, you could setup a matrix, I.E. a 4-to-1 connected to 1-to-4, to route your signals to different locations.
Of course you need to come up with 1/8" or 1/4" to RCA adaptors as needed.

I'm often switching between my headphones plugged into Gameboy, Headphones plugged into iPad and headphones plugged into my computer and my monitors…It's a tangle of cords and just annoying overall.

I tried searching around and aside from a pro studio rack, I was wondering if there is any sort of device that would allow me to plug in my various inputs and then have my headphones / monitors as the out (even if it was just 1 out for headphones I could live with it) and then I can just push a button to route the audio from gameboy or computer or iPad into the headphones?

Maybe i'm just not searching for the right thing…maybe I'm just lazy about plugging and unplugging things...