If watts exceeds rating?
Let's use another example: I have a 100 W light bulb that I'm going to plug into the Irish national grid which has a capacity of 5 GW at peak capacity. Do you think it will burn out my bulb?

Answer: No. The bulb will draw the current it requires. This current is limited by the resistance of the bulb filament.

Back to your question:


  I have a 2 watt rated ball valve, 
  and I have a 12v dc 1 amp power supply. W = a * V. So 12 watts power supply? Would it burn out the ball valve?


No. It will provide as much power as the solenoid valve requires. The current (and therefore the power) will be limited by the solenoid resistance.