I really want to upgrade my Hard drive for my PS3 but I am worried about losing my games. The only way I can think of is basically getting Plus and backup all my games right before putting the new hard drive in.
Is it saves or your actual downloaded games? If you get + then you can upload saves to the cloud(backing them up) but not actual games. However once you change hard drive you can just go into your download list and re-download them. There are other ways but idk how you do them, maybe try google.
The only way to backup complete games from your PS3 console is to connect an external USB HDD & use the Backup Utility: http://manuals.playstation.net/document/en/ps3/current/settings/backuputility.html
Then change/upgrade your internal HDD, followed by connecting the external USB HDD & using the Backup Utility again but this time selecting "Restore". That will definitely include any copy-prohibited game saves along with everything else you'd expect.