Facebook has become a part of life for a majority of its users. We share so much of our personal information on it that we cannot afford to let our account fall prey to hackers and identity thieves. So I would first suggest you to make passwords stronger by using a combination of letters (captial and small) numbers and if possible symbols and please make sure you passwords is at least 8 characters in length.
Its best to create a new Email ID for facebook or use and Email which no one or very few people are aware of,cause your account can only be intruded if the intruder knows your login email in the first place.
Making password strong is one thing but protecting it is another thing. At some point you might need to log into your Facebook account from an unknown device /computer from a cybercafe, school, college or may be your friends computer these devices are not in your control and you never know if a malicious software like a keyloggers etc. is installed on it.
New facebook features
Now you don't have to worry too much about secuirty , a couple of days ago facebook rolled out new features. First feature is the one-time passwords which is a US only feature (It is expected to come to other countries soon). With this feature if you have saved your mobile number on your facebook account all you have to do is text "otp" to 32665 from your mobile phone. You will shortly receive a temporary password which you can use to log in to your account, this password will only work for the next 20 min after it has been received.
The second feature is the remote logout feature. Sometimes it happens that you log into your account from your friends computer or mobile device and accidentally check the "Remember Me" box. Or forget to logout from your account, in that case you might be still logged into the device. With the new feature you can keep a track of which devices you are actively logged in by going to Account Settings>Account Security, If you are logged /active on other devices it will show up. You can simply click "end activity" to logout of that device.
The third most effective and important feature is the Activity log/Account Activity, if you have a Gmail account you might be familiar with this. Go to Account Settings>Account Security you will see Login Notifications where you can opt to receive notifations as email or a text message whenever you or any other uninvited person logs into your account.
Account Activity shows you info of the last login activity which includes location (based on ISP/IP), date & time, the browser used and the OS (operating system) used .
After the privacy issues that sparked up earlier this year, Facebook is definitely trying to improve its image by give its users premium features. This will create a safer environment for people to share their information online. Any problems or anything you would like to share, put it in the comments.