Can I make my own backup?

Not really; Linode backups are on-site, but not on the same machine as your linode. Many of the scenarios that might cause you to lose access to your linode would also cause you to lose access to your backups on that linode. Example, disk failure in host machine.

@cfauver:

Just wondering, I do not need anywhere near the storage I have on my server.. is it possible for me to create my own backup making an extra partition on my linode and using some sort of backup program? Would it be just as good as paying Linode to use their backup option?

You can but like Guspaz says you it won't protect you from everything a proper off-site backup will. There is nothing wrong with taking your Linode down and cloning your filesystems every once in a while but for real backups you need the data physically distant from the Linode.

I do BackupPC backups to home every night, If my Linode went down and never came back up I'd only ever lose less than 24 hours worth of data plus the time it would take to setup a replacement system.