Facebook launched a new feature which will help prevent unauthorized log ins to user accounts. They've introduced a second step to the login process. If you turn on this feature, you'll enter your email address and password as usual, but then they will have a security code sent to their mobile phones. This short numeric code will need to be entered to access Facebook. You can then authorize that computer as a trusted device and will not have to enter a code again. If you lose your mobile phone, you can still use a trusted device for Facebook and also use it to authorize a new device.
Upping security with login approvals
If you ever use Facebook again on a new device, the whole process will repeat where you get a text message on your phone and you enter the code. If it's someone other than you whose logging in from another device, you'll be able to change your password immediately as you'll get a text to your phone when they attempt logging in letting you know that your account information is compromised. To enable this feature, go to the Account Security section of the Account page, and go to Login Approvals.