Busy? On vacation? Let your teammates know you're occupied with a simple Slack status. When your work is getting on top of you, it's easier to let everyone know via a status. Otherwise, that's just one more thing you have to do when you don't have the time to.
Setting an out-of-office / vacation reply to people who send you an email is polite and lets them know that you won't be answering their email until you return. Google's Gmail platform makes it easy to set up this automatic response and remove it once you have returned to your office.