My mug I used in office had a lot of coffee and tea stains along the walls. I remembered reading somewhere that these stains can be cleaned by all-purpose-cleaner-baking soda. I thought I could try it over the weekend. Many articles recommended scrubbing the stains with baking soda. I did not want to put in much effort and added a spoon or two of baking soda, some detergent and filled the mug with water and let it be for 2 days.
Ta da! All the stains are gone and my mug is clean. I was not sure how well it would work and I did not take a before pic but I do have an after pic. So, here it is.
Try it with your mugs if they need cleaning!