To play commercial DVDs in Ubuntu you need to install libdvdcss for recognizing them, libdvdread4 for reading them and libdvdnav4 for navigating them. These are not included by default, because Canonical would have to pay a royalty, making Ubuntu non-free. For personal use however, they are free for you to install.
In a terminal window run
Afterwards, and again in terminal run
sudo apt-get install libdvdcss libdvdread4 libdvdnav4
Rebooting might be necessary.