If city water is used and properly stored in an air tight container it will not "go bad". It will however over time go "flat". Before drinking if you want it to taste more normal shake it up in a bottle and then poor and enjoy.

Well water on the other hand may taste weird or different but it still won't go bad... this is all dependent upon the type of water coming from your well, if it's filtered, hardened, softened, etc, etc.

Also, keep in mind you can just boil the water if you think it may have gone "bad"...