I want to use arduino with 3.3V on the external circuit. But it doesn't work. I'm using 16mhz crystal. Should I change it and is it necessary to make changes on the bootloader.
As you lower the voltage it's necessary to lower the clock frequency. The chip data sheet should tell you what voltage is needed for reliable operation at each frequency.
First, how are you supplying power?? 3.3V to the "5V" and Gnd pins??
That may cause problems with the USB interface. Can you load "Blink"?? Change blink speed?
Our Arduino-compatible version HERE: has a separate 3.3V regulator. It has a jumper that can switch the 328 chip operating voltage to 3.3V, and also supplies 3.3V to the 3-pin connectors for I/O, making it easy to interface to 3.3V-only devices. The USB interface/download still runs at 5V.
These "YourDuino Robo1" have run for days at 3.3V and appear to be fine. This is on the edge (or over the written spec limit) at 16 Mhz, but is working successfully for quite a few users.
YMMV of course... but it appears workable.
As always (Disclaimer: In My Limited Experience) Robert is Right. 
From my years designing chip testers that could "shmoo" times, voltages, pulse levels and rise/fall times etc. all over the place, I'm sure that the "guaranteed spec" value is one thing, and the actual performance is another. "OverClocking" is a recreational activity for some
Also, there is evidence that mature designs on mature fab lines usually "beat the spec" by quite a bit.
But that ain't guaranteed!
We had forum discussion recently where underpowered serial would not work, raising the voltage solved the problem. So somethings may work when underpowered, & some may not.
underpowered serial would not work,
Yes, the version I showed needs 5V for the USB Serial interface...
The "safe" answer is to just use the 8MHz Pro Mini
http://www.ebay.com/itm/New-Mini-ATMEAG328-3-3V-8Mhz-Replace-ATmega128-For-Arduino-Pro-Mini-Compatible-/191182699659 or the Sparkfun one: https://www.sparkfun.com/products/11114
That being said, I have never yet had an issue with 3.3V and 16MHz even with serial 9600 BAUD... Using the design at 65F to 76F in the house. Outside, who knows? I'm old and crotchety and I don't like too hot or too cold... And I keep my microcontrollers in the same environment.
Ray
Using the design at 65F to 76F in the house.
Interesting point. It's not easy to do large temperature variations without significant equipment. One tester I designed had an optional wafer prober (X-Y table that moves a full wafer of chips) that had capabilities of (I think) -30C to 150C on a wafer. Had to be flooded with dry nitrogen to keep condensation off the chips at low temp. I think that unit was $22,000 in 1990 dollars.
I will try some high-temp test on a regular 328 at 3.3V and 16 MHz. Can anyone suggest a good test sketch that might find internal errors.?
I have THIS: test, which runs some code and tests each I/O for source and sink capability, and the Analog inputs at a couple different voltages. Hmmm. I never ran that at 3.3V yet.