You should, at the very least, be rinsing it out on a daily basis after drinking your coffee and especially if that coffee had cream and sugar in it. And this is only if you don't have the facilities for actually cleaning it out with soap and water.

Otherwise, bring it home and wash it out every night so it's fresh and clean for you the next day.

Do this, and your mug can last for years. I've got a stainless steel mug that I've had since 2001 and while it's been abused, it still works.