I would like to create a synthesizer using 20 separate piezos for the triggers. In other words, each piezo would trigger a separate tone. At the very least I would like to know if connecting 20 piezos to an arduino is realistic and how to do it. I know there are only 5 analogue inputs. Perhaps instead of each piezo triggering a separate tone, each could trigger the next tone in a cycle. That way perhaps all of the piezos could be connected through only one analogue input. I'm just not sure if this is possible or not. Any advice would be appreciated. This tutorial represents what I would like to do, only my idea calls for a larger scale (http://arduino.cc/en/Tutorial/Tone3
I have no idea what you have in mind when you say "each could trigger the next tone in a cycle", but sampling that many inputs doesn't sound practical to me. Replace them with simple switches and you might have something that'll work.
What do you have in mind for the output? Are you going to put out a simple tone / combination of tones that an Arduino could generate, or are you hoping to play back samples? Are you expecting to support simultaneous notes and any effects on the sound, or just recreate a stylophone?