Alan Stein built this $10 Arduino beatbox for his first Arduino project. Requiring just three resistors and a piezo speaker (in addition to the really bare bones board he is using), it uses capacitive sensors instead of expensive buttons to keep the cost down. He also has a nice comparison of the Arduino to his longstanding favorite, the PICAXE. Source code and schematics are available at his website.
$10 Arduino beatbox uses capacitive sensors for buttons