MakeMKV is the only utility that I've found that is capable of playing (and copying) Blu-Ray movie releases on any Linux, including Ubuntu. I'm quite sure MakeMKV can also handle DVDs, so it might be your one-stop solution for the conversion process. It has a simple GUI and a command-line utility. By default the GUI will choose a title (or titles) for you based on some heuristic, and put the corresponding original MPEG stream inside a MKV container.
MakeMKV has closed source parts, which are proprietary software. You can use it for free for 60 days, after which you will need to obtain a license key. This key can be bought from the author (currently USD 50, I think).
If you do not wish to compile the sources, I think you can get an installer from ebower's PPA (it appears to cover everything from 10.04 to 12.10):
sudo apt-add-repository ppa:ubuntu-ebower/ebower
sudo apt-get update
sudo apt-get install makemkv-install
However, I have no experience using that PPA.