For my project, I'm looking for a button that can have more than two states. I am aware of a push button, which can either be pressed or not pressed. I am looking for an "analog button" i.e. a button that can be not pressed, quarter pressed, half-pressed, etc. Does a button like this exist? I know Gamecube controllers have something like that, but I haven't found anything online. If anyone knows the name of such a component or something similar to what I'm looking for or can at least point me in the right direction, I would appreciate any and all comments.
It reminds me of those high end analog optical keyboard switches:
On the less exotic end of the spectrum, and perhaps not at all what you are interested in, would be a force sensitive resistor (FSR).
Perhaps a slide potentiometer with detents. You may have to fashion the detents. Should not be that hard.
groundFungus:
Perhaps a slide potentiometer with detents. You may have to fashion the detents. Should not be that hard.
What are detents and why are they important?
And how would I fashion them?
Detents are a mechanical means to divide motion into discreet parts. As in the clicks of a rotary switch or encoder. Mechanically defines positions.
I think what you're looking for is called a "plunger pot/potentiometer" e.g. Plunger Pot - 4QD - Electric Motor Control That's one's expensive but there are cheaper versions.
Steve
hillo111:
I am looking for an "analog button" i.e. a button that can be not pressed, quarter pressed, half-pressed, etc.
First critical question - why?
But Steve has clearly provided the solution in any case. 
As "Deep Thought" said in The Hitch Hikers Guide to the Galaxy, “you are really not going to like this answer”. It is a plunger type and you push it down and when you release it the plunger returns to fully out.
Guess what bit you are not going to like before you click the link. It is exactly what you want / need.
The description that talks about this as being rotary is simply wrong. I have one of these it's a plunger.
Paul__B:
First critical question - why?
Of course, the question stands. But I just thought I'd point out that camera shutter buttons are often like that - light press to focus and set exposure, full press to shoot. Maybe you can find one of those somewhere.
How about a button with a small magnet, moving towards two reed contacts?
And what about the button in an electric screwdriver or drill? They are often analogue: the more you press the faster it rotates. Even the low end cheap tools have this. I don't believe half of the cost is the button.
Do you have any 3D printing skills?
A rotary encoder would meet the electronic requirement but not the push button requirement. I'm thinking a cog and pinion mechanism made by 3D printing to convert linear motion to rotary. They would be a cinch to make. The challenge would be a housing for the encoder and plunger. Needs a spring mechanism -- maybe a spiral spring on the cog over the encoder shaft or a straight spring under the plunger.
John.
Something like this switch found on Ali Express?
Cool. I didn't need to post and then re-edit/modify to make the images appear! 
Cheap membrane switches use a carbon-filled pad on the membrane underside that presses
onto gold-plated traces on the PCB part. The resistance will depend somewhat on the pressure,
especially if the traces have significant area such that the pad contacts more of the PCB trace
with more pressure.
I think this resistance is used in some games-controller units to give (somewhat crude) analog
inputs for push-buttons.
However its not a standalone part you can buy.
For many cheap MIDI keyboards with after-touch there is a load-cell monitoring the pressure
exerted against the whole keyboard assembly - by combining this value with knowledge of
which keys are down gives MIDI aftertouch information. You could do something similar for
push buttons perhaps?
Or like this, simple and cheap: 2 Buttons And a Stick. 
Youtube: Two analog buttons to create one that can be half-pressed. - YouTube
