Moving a project off the Arduino?

some links:
http://www.arduino.cc/playground/Learning/Standalone

http://www.arduino.cc/playground/Learning/AtmegaStandalone

It's also possible, I think, to program the chip in the arduino board you already have, then pull it out and put it in the circuit that you want. Overall, though, even with an external programmer, the project is simple enough to do.