Electric guitars uses switches to select which pickups are activated at a time. Most designs though do not allow for all possible combinations of pickups. Also there are alternative ways of wiring a guitar, series/parallel wiring changes the tone. Also reversing the phase (polarity) gives you other sounds. Almost no guitar gives the option of selecting all of these options because the wiring becomes too complex. I would like to challenge Ben to create a system by which an Arduino can be used to select any of the different combinations.
Here are the wiring diagrams to give you a idea.
Series/parallel switching.
http://www.premierguitar.com/articles/Adding_Series_Switching_To_Your_Strat
In-Pase./out of phase
Current mods to help add pickup combinations include:
If you put all these ideas together you get something like what Brian May from Queen built. http://www.premierguitar.com/articles/21307-mod-garage-inside-brian-mays-red-special
Still there is more, pickups with two coils, called "humbuckers" can be "coil tapped" to be single coils, making one more set of switches one might want.
I have a Music Man 'Steve Morse' guitar. http://www.music-man.com/instruments/guitars/steve-morse.html
It has 4 pickups, and switching between them is crazy complicated all by itself. Here is the diagram: http://imgur.com/r5As604
Finally another guitar mod is know as a 'kill switch'. It's basically just a momentary button used to cut the signal to the amplifier, but when used by people like buckethead uses https://www.youtube.com/watch?v=NM8DuJKYlqE
A micro-controller would automate a killswitch and have lots of selectable patterns.
Can you help me Ben? Can all of this be built on to one circuit board controlled by a microcontroller? Possibly even with an LCD display that indicates what mode it's in?