You should log out before leaving your session. This clears the memory so no one else can access what you were doing and you don’t expose yourself to security risks.
If you are using a free web-based email service such as Yahoo! or Hotmail, your email is reasonably private and secure. Refer to the help pages for your chosen email provider.
If you are buying an item or a service from a company, check the transaction is on a secure server – you will see a padlock on the screen and the address will start with https://. If you’re logged into the website, make sure you log off afterwards.