How to remove coffee stains from the bottom of a dirty old mug?

I have several 'mugs' most I use, others I simply offer to guests when entertaining... none of them have stains but was unfortunate enough the other day to drink coffee out of someone else's mug and there were dark STAINS, I didn't realise it was theirs... anyway I survived and want to know if anyone knows of a natural solution to the problem with the stains, a herbal remedy or salt crystals or should I go out and buy some designer mugs and use the old one as a vase or garden ornament what would YOU do?