I used to use vinegar (and vodka, at one point, then I ran out) but read that it can corrode the silver backing to the mirror if it seeps under the glass.
I clean mine with a damp cloth dipped in warm water and white vinegar and dry/polish them after with a soft, old linen tea towel. We have mirrored wardrobe doors that get covered with hand prints (and dog's nose prints) and it brings them up a treat.
Narta I am puzzled why you need advice on this matter. is there something hidden in the question that we are all missing, or how is it that you have never seen any mention of glass cleaning anywhere before?
Spray of Pledge multi-surface on mirrors and glass doors throughout the house, buffed with a microfibre cloth. Not the most environmentally aware method, but the way I've done it for years!