Never again will you have to dismantle a finished project just to reuse an Arduino board!
This tutorial will go through the steps involved in fabricating your own Arduino-compatible circuit using just ~$8 of parts (this includes the ATMega chip!). This is perfect for installing and embedding in permanent pieces, as you don't need to waste a full $30 Arduino board in a project you will never need to reprogram or touch ever again. It is also great because you can solder any custom circuits (LEDs, other ICs, any external analog circuit) on the same board, and customize in terms of shape and size.
I assume you have a regular Arduino board already, so pulling out the chip to reprogram it shouldn't be a big deal, since we're going for minimal parts here. You could even go simpler by leaving out the reset button! To better illustrate the process, I did all the wiring on top of the board for tutorial purposes, but feel free to save yourself some space and make some of the connections on the copper-clad side of the board, as seen on hackduino.org or similar.