Linux Mint 18 comes with the Guest user enabled by default. With a guest user, you can login to a Linux system without using a password. While this feature could be very convenient in a family setting, it’s a good security measure to disable it if you are not going to use it.
In Linux Mint 18 (I have tested this on Linux Mint 18.2 Sonya), you can disable the Guest session by going to Menu > Control Center > Administration section > Login Window.
After you click on Login Window, enter your administrator password and toggle the button next to Allow guest sessions to OFF (it’s the last one in the list).
After doing this, reboot your system and you won’t see the option to login as Guest the next time.