Do you have a 0.1uF across +5 and GND as close to the processor's power pins as possible?
Do you have any fast-switching digital pins close to AVCC, AREF, or the Analog Input pins?
Did you try a capacitor on AREF?
Have you checked Grumpy_Mike's website for de-coupling advice?
AREF is not connected on the diy bb arduino (see previous response)