In Facebook, click on the tiny gear sign on the top right of the page, go to ‘account settings’ and then to ‘security’ on the left pane. Under ‘security settings’, click on ‘active sessions’.
No one else might be using your account, but you would not have logged out of Facebook, leaving the session active. Anyone can gain access to your account in such circumstances. To remote log out, click on ‘end activity’.
In Gmail, at the bottom right side of the page, you will see details of your latest email access. If someone else is simultaneously using your account, you will see a notification there.
Click on the ‘Details’ link below it. A new window opens, with a notification on whether the account is simultaneously open elsewhere. Like in the case of FB, you might not have logged out of the account, leaving it active. If so, you will see an option to ‘log out of all sessions’. It also shows you the details of your previous 10 accesses to the account.