After every cup of coffee. If I just finish one cup and want another, I will just rinse it with water. But if its not beeing used in a little while it will be washed with soap.
For mugs and thermoses, I think it's crucial that you wash with soap & water with a bottle brush such as this OXO. The famed 17oz Zojirushi desperately needs one since its neck is so narrow. I'm pretty OCD about re-usable bottles collecting odors from tea and coffee, and it gets the job done. If I'm in public, I try to at least rinse my thermos with water ASAP.
Coffeemugs are resusable for about a day after they have not been used. I usually end up grabbing a new mug, but I have no issue with rinsing out a day old cup and giving it another go.
Usually washed after every drink change. If I'm just about to put exactly the same thing in it I don't bother to rinse it or anything. But it usually ends up getting cleaned pretty regularly.
Coffeemugs are resusable for about a day after they have not been used. I usually end up grabbing a new mug, but I have no issue with rinsing out a day old cup and giving it another go.