The Arduino is already inexpensive ($20-$40), but the basics can be implemented for less than $10 if necessary:
Here is a recipe for using the atmega168 as a standalone Arduino. It uses the internal oscillator of the Arduino running at 8mhz, and is powered at 3.3 volts.
http://hcgilje.wordpress.com/resources/arduino-standalone/
http://sustburbia.blogspot.com/2010/08/diy-arduinos.html
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