I have an acrylic guitar that I want to stick LEDs inside of, but I want them to light up when I play. Any ideas?
the maximum amount of LEDs that would be used would be 3 and the whole thing would need to run off of a 9-volt battery. so any ideas?

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That runs off a 9V battery and uses an iPod headphone port for power, so you might even be able to use the guitar output directly. Not sure how hot a signal that is, you might have to tap into the amp.
If you could get the signals to work, you might even be able to do fun things with separate banks of light for each pickup, or each string. That would probably be an even weaker signal, though. I'm not familiar with electric guitar circuitry.
Also, it'd be great to have more than one LED color, so could I create the same circuit in that 'ible, but with two red LEDs and two blue LEDs?
. Probably. Use a pre-amp with a high impedance input and loss/distortion should be minimal.
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> Or would it be possible to wire in a small microphone to pickup the sound instead of a headphone jack? would that require an amp for the mic?
. Very possible. You will probably need a pre-amp, but may not need one for something like a piezo.
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. Combine that with the link CameronSS provided earlier (you can find more sophisticated circuits, but that one should work well for your purposes) and you should be good to go. Everything, including a 9-volt battery, should fit comfortably behind the pick guard.
you may have to use a 12v battery as well but i think it would be worth it
a little info on connecting a darlington array
http://fritzing.org/projects/arduino-knight-rider-with-8-blue-12v-led-modules/