Backing up files before restoring a computer to its factory settings is important, else we might regret losing important data. Even when consciously backing up data, we sometimes forget save some important things. Here is a list of some things I do/save before restoring my computer to factory settings.

Places to check:
1) All partitioned drives
2) Desktop
3) User folders - Documents, Downloads, Pictures, Music, Videos 
-----> I don't usually save things in User folders, but once in a while I save 1 or 2 important files to it. So checking it won't cause any harm.
4) Any applications that save files - webcam, chats. Check the hidden folder "AppData" in the User folder for such files.

1) Bookmarks - Firefox, Chrome, Internet Explorer or any other browser
2) Take note of any add-ons in use
3) Save data of any add-ons in use - ScrapBook (for me)
4) Saved Passwords - for Firefox: Password Exporter add-on 

1) Windows Calendar
2) Sticky Notes

With all these saved, it is save to restore the computer. I recommend not restored all this files back on to the hard drive once the computer is restored. Try starting fresh, and be more organized every time.

Please add comments if I missed anything that needs/is safe to save/back up.