I have a Hot Water Boiler and hot water heater that are constantly going out (pilots) They are both natural gas and use the same chimney from the basement. Any thoughts or suggestions? Sometimes wind is a factor other times it is not.

Adding a cap on the chimney may help if you don't have one. You could try replacing the thermocouples and turning the pilot up.

I also believe that the pilot going out can indicate the heat exchanger coils need to be cleaned, I lost a set of eyebrows once due to a dirty furnace.

Down draft from the chimney most likely cause. See labman for the chimny cap answer.