Totem is the official movie player of the GNOME desktop environment based on GStreamer.
Ubuntu, a popular form of Linux, launches Totem by default when you insert a DVD into your workstation's CD/DVD tray. However, by default, Totem doesn't contain the proper codecs to play DVDs. When you first play a DVD, Ubuntu will ask whether you want to search for the proper codec. If you choose to search, Ubuntu will offer the available codec programs in the repositories for playing DVDs.
However, you may not be able to view your DVD even after installing the proper codec. Watching a DVD in Linux is a bit of a legal quagmire if you live in the United States. The Digital Millennium Copyright Act (DMCA) and other issues make it tricky for any open-source program to navigate the licensing maze when it comes to movies that are encoded or otherwise protected against pirating.
Not all DVDs have these features enabled, so you might be able to watch some DVDs on your Ubuntu workstation. If you burn your own DVDs, they should work just fine.