As simple as this one sounds, you'd be surprised at how often employees leave and the people left behind -- as well as clients -- have no clue.
This likely happens more in bigger companies where communication can often fall through the cracks, or during summer when lots of people are out on vacation. But there are times when workers have tried to reach someone within the company because they're collaborating on a project, only to find out the lack of a response is because the person has left the company. Don't let employees and clients find out you're gone from someone else. Reach out and let them know via phone or email, and don't forget to put up an out of office explaining what's happened on your email system.
This also serves as a great way to thank everyone you worked with over the years while you're informing them of the news.