Command line help

Additional information might help:

Do you actually have a /dev/sr0? Depending on the operating system, the number of devices etc. the name may vary.
Does the user that is executing dvdbackup have permission to access the device?
Can you watch DVDs using vlc?
Did you get any error messages from dvdbackup?

Yes, when I use Handbrake it reports that it is using /dev/sr0...
My permissions are set correctly
DVD's, CD's all play correctly in VLC, or any other media player I've tried... I normally use Handbrake to archive my DVD's, just thought I'd give dvdbackup a try...

What is the output of

ls -l /dev/sr*

brw-rw----+ 1 root cdrom 11, 0 Aug 30 05:39 /dev/sr0

Have you read the man pages for dvdbackup?

http://manpages.ubuntu.com/manpages/trusty/en/man1/dvdbackup.1.html

...
-i DEVICE, --input=DEVICE
where DEVICE is your DVD device. This switch only needs to be used if your DVD device node is not /dev/dvd
...

What do you get for the command

dvdbackup -i /dev/sr0 [other options]

When I enter the command you replied with the result is just a display of the Help page. It doesn't indicate what is wrong... Here are the results when I copy and paste your syntax into a terminal window:

<SNIP>
HP-Pavilion-g7-Notebook-PC:~$ dvdbackup -i /dev/sr0
Usage: dvdbackup [OPTION]...

  -h, --help display this help and exit
  -V, --version display version information and exit

  -I, --info prints information about the DVD
  -M, --mirror backup the whole DVD
  -F, --feature backup the main feature of the DVD
  -T, --titleset=X backup title set X
  -t, --title=X backup title X
  -s, --start=X backup from chapter X
  -e, --end=X backup to chapter X

  -i, --input=DEVICE where DEVICE is your DVD device
                           if not given /dev/dvd is used
  -o, --output=DIRECTORY where directory is your backup target
                           if not given the current directory is used
  -v, --verbose print more information about progress
  -n, --name=NAME set the title (useful if autodetection fails)
  -a, --aspect=0 to get aspect ratio 4:3 instead of 16:9 if both are
                           present
  -r, --error={a,b,m} select read error handling: a=abort, b=skip block,
                           m=skip multiple blocks (default)
  -p, --progress print progress information while copying VOBs

  -a is option to the -F switch and has no effect on other options
  -s and -e should preferably be used together with -t

Report bugs on Launchpad: https://bugs.launchpad.net/dvdbackup

Thanks Benjamin Drung, that solved my question.