Do you have your work email on LinkedIn? If you use it to log into your Linkedin profile (or it's the contact email visible on your profile) and you are changing jobs, remember to change it before you finish up.
This might seem like a no brainer but it's easy to forget and once you no longer have access to that work email account, changing, updating or even accessing your LinkedIn profile can become a real pain. Especially if you forget for a while and are a couple of job changes in. (Duplicate profiles anyone?)
And when an employee leaves, often their work emails are forwarded to another team member, so having someone else receive your LI messages definitely isn't ideal.
Plus think of all those annoying recruiter inmails you are missing