I am wanting to remove the chip from the arduino board after i program it and place it in my project by itself, all i need to do that is the chip a 16MHz resonator, and a voltage regulator right?
A few capacitors and a resistor or two wouldn't go amiss. 0.1 uF decouplings and a couple of electrolytics around the voltage regualtor. A 10k resistor to hold the reset high.....
I'm pretty sure the 10k resistor is unnecessary as there already is a pullup resistor inside the AVR (see Figure 10-1 of ATmega328P datasheet).
The 0.1uF decoupling caps (ceramic!) are a good idea.
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The Gadget Shield: accelerometer, RGB LED, IR transmit/receive, light sensor, potentiometers, pushbuttons
I didn't find the reset pin has a pull-up resister anywhere in the atmel document last time I went looking for it. I specifically add a resistor as a result. Here, read this tutorial from NYU:
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The Quick Shield: breakout all 28 pins to quick-connect terminals
If you know what you are doing the bare chip will suffice.
If you do not need precise timing the 8MHz RC Oscillator is good enough.
If you have a HV programmer you do not need to pullup reset - you can completely disable it by proper fuse settings. But do so at your own risk. This is a way to lock you out of the chip.
If you have 4.5V-5.5V supply (or slightly lower if you are running @8MHz) you can get rid of the regulator as well.
It all depends on what you are doing. If you do not fully understand what is going on you can not get rid of the caps though.
Udo
Thank you RuggedCircuits. I only read through the text and found all GIO pins have pullups and reset pin has no description of a pullup so I assumed no pullup. There should be no way to disable this pullup, right?
While there is a way to disable the entire reset functionality, I don't know of a way to disable the reset pullup.
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The Gadget Shield: accelerometer, RGB LED, IR transmit/receive, light sensor, potentiometers, pushbuttons
No, there is no way to get rid of it. This is why they have a quite weak pull-up there (around 47k), that can easily be overridden in both ways.
The reset logic is well documented, there is much more than just figure 10.1 in the datasheet 
As Uwe said, you need nothing around an ATmega... And the internal 8MHz calibrated RC oscillator is VERY precise.. However it depends on the temperature....
I was talking about external components. My point was that disabling the reset pin will get rid of the requirement for an external pullup.
@deSilva: what exactly do you mean by "very precise"? How precise? I do not get how "very precise" and "temperature dependent" fit together.
Udo