I have purchased an ATMega328 from SparkFun with the Arduino bootloader pre-programmed. My intention is to replace the ATMega168 I currently have in my Duemilanove. Is this as simple as swapping the chips, or will I need to take any additional steps? As I recall, I am currently at Arduino 13 but am planning to upgrade to 17 (current version) concurrent with the part swap.
Yes, you may simply switch the chips. Version 13 implemented support for the 328, so an IDE upgrade is not essential.
Make sure you change the "Tools/Board" setting in the Arduino IDE to "Arduino Duemilanove or Nano w/ Atmega328"
Yes, you can just swap it in. I've also upgraded a Diecimila without any problems. If you have an AVR programmer (such as the one from Adafruit) you can also upgrade it with a fresh unprogrammed chip.