Considering the already low price of the Arduino board, building an Arduino-like board yourself probably doesn't save you any money but is certainly a fun and education project to do.
I tried to make the simple board even simpler, by using a Serial instead of an USB Port, the ATmega's internal clock instead of an external crystal, and requiring 5 VDC instead of providing any kind of power regulation. However, my board does expose the 6 header ICSP, equivalent to the one available on the original Arduino NG Board.
RadioShack's Multipurpose 417 Holes $1.79 PC Board (Model: 276-150 Catalog: 276-150) built a great starting point for this electronics project, which was obviously inspired by Tom Igoe's 'Arduino Breadboard'.

After soldering the components onto the board and checking all joints, it was time to put the Arduino bootloader into the Flash Ram, which raised a couple system / software related questions I hadn't thought much about before:

• To be able to use either the ATmega8, which is used on the original Arduino, or the pin compatible ATmega168 microcontroller, which offers twice the amount of internal RAM, I had put a 28-Pin DIP Socket on the board. While the original Arduino board uses an 16.0MHz external crystal, my board relies on the internal clock, which for the ATmega8 means a 1.0MHz Internal RC Oscillator (slowly rising power) and for the ATmega168 an 8.0MHz internal RC oscillator, which by default however gets divided by 8, resulting in 1.0MHz system clock. How could I address the speed difference, to keep software changes to a minimum?
• Since this obviously involved messing with the ATmega's confusing fuse settings, what fuse bits do I have to adjust?

Let's address the last question first and take a look at the fuse bytes. The content of those fuse bytes persists reprogramming of the Flash memory and almost every bit in those fuse bytes represent some kind of status setting that configures the microcontroller, for instance to work in concert with other components on the board. Oddly enough, for all fuses '1' means unprogrammed while '0' means programmed.