Whichever voltage reference is being used (AVcc, external voltage applied to Aref pin, or internal bandgap voltage(s) ) it will be seen on and can be measured at the Aref pin when selected. That makes for a good common spot to add a .1ufd bypass cap. Not all boards include this cap. I have both a Seeeduino mega board and a clone RS-232 mega328 board which do not. If I run a continuous analogRead() with a good regulated clean voltage applied to the analog input pin and print the results to the serial monitor I see a +/- single count flicker at all times on the 328 board, but just a stable reading on the mega board. I soldered a .1ufd cap from the aref pin to ground on the serial board and then it to became flicker free.
As Grumpy said other things that can effect the A/D conversion noise. Such as filtering method on the Avcc pin, layout of the grounds between the analog and digital runs, source Vcc noise, etc. It all relates, however being only a 10 bit A/D conversion it's not too hard to tame it to be useful to the resolution possible with only a 10 bit conversion.
Lefty