sjheiss:
What I mean, is can I reprogram the microcontroller without a breadboard, second microcontroller, or a dedicated programmer. Just using a computer, the Arduino, and the chip it came with.
Most Arduinos are self-contained in that respect and so only need a computer and a USB cable, so yes. Exceptions that I am aware of include the Arduino Pro and Pro Mini (these require an FTDI cable or equivalent breakout board), there may be a couple others, see http://arduino.cc/en/Main/Products for details. Apologies if I am restating the obvious.