I've got a couple of Duemilanoves which I use for quick prototyping and testing. Bigger and/or more complex projects are moved to separate breadboards with standalone Atmega368P-chip and separate powersupply.
But, I'm experiencing that the Duemilanove resets the microcontroller frequently(every third og fourth second). This only happens when it is connected to USB(Arduino software does not need to run on computer). If I power the Duemilanove with 9-12v it works perfectly.