I always found that when I'd clean my mirrors, every product I'd use would streak. Well, I found something that doesn't and it's cheap. Water! I just wet my cloth, wipe down the mirror and use either a torn up sheet or paper towel to dry it.
Shaving cream has a second life as an easy to use cleaner for bathroom mirrors and fixtures. You do not need to buy an expensive brand. This is a page about cleaning mirrors and bathroom fixtures with shaving cream.
Cloudy mirrors can be the result of a residue build up on the face of the mirror or damage to the backing. To clean your cloudy mirror try either foam shaving cream or straight white vinegar in a spray bottle.