As mentioned, tar can create multi-volume archives. Alternatively you might want to take a look at split command, if you truly want to go ahead with your current backup plan.
But, please remember that main purpose of taking backups is not to backup, but to be able to restore as quickly and reliably as possible. Recovering archives from many DVDs, hoping that each of those discs are OK and praying that restoring the multi-volume archive goes OK, doesn't sound like fun.
Not to mention another important job of taking backups: you need to test them somewhere regularly. Again, restoring from the DVDs doesn't sound like fun and due that laziness might creep in and lead to situation where no one doesn't test the backups at all.
Get instead a HD or couple of them. It's up to you if that's an USB HD or what, but copying to HD is much faster and much more reliable than using optical drives. Also tasks like recovering only a handful of files instead of every file becames easy. The already mentioned rsnapshot mentioned is a very nice tool for taking backups. If you have several servers to back up, other good alternatives include Bacula and BackupPC.