Yes! You can download a copy of your facebook data!
Click Account Settings
Under Language find the link Download a copy of your Facebook data. Click it.
On the next page click the Start My Archive green button.
Once the button is clicked you need to wait for sometime (can be a few hours too depending on the content). Once the download is ready you will be notified via email. You can also return to this page and check the status.
Once the download is ready you just need to click the Download Archive button and download the zip from this page.
Unzip the file and you will find an HTML file (index.html) and two folders (html and photos). You can run the index.html file which will show you all the links to the downloaded data. Also you can explore the photos folder where all your albums and images are stored.
Make sure you keep the downloaded files in a safe place as it contains all your personal data and can be accessed without a password.