It's not too difficult to setup DVDFab under Linux using Wine, but there are a couple caveats. It seems the settings cannot be modified from within Wine. Wine can't interact with the configuration menu. This is a problem because DVDFab automatically starts previewing any DVD it finds, which causes Wine to lockup.
So, we need to disable this automatic preview. First, run the DVDFab setup program with wine (wine DVDFab5230.exe). I disabled the VSO burning engine and the desktop/quick link shortcuts. You will need to start the program once to make sure the registry keys are created. You can do that by typing wine "C:\Program Files\DVDFab 5\DVDFab.exe" into a terminal.
Now you need to edit the registry. Start wine's regedit program via wine regedit.exe. In the HKEY_LOCAL_USER key, open Software, then DVDFab, then V5, and finally Generic. There you will find two options, PreviewAutoPlay and PreviewAutoShow. They are set to 00000001 by default. Change them to 00000000.
Now, before you start DVDFab, you will need to mount the DVD you want to rip. Also, if you haven't configured wine for your drives, you will need to do this. Run winecfg and select Autodetect from the drives tab.
Finally you can run DVDFab (wine "C:\Program Files\DVDFab 5\DVDFab.exe").
P.S. I don't know if Blu-Ray or HD DVD ripping work since I don't have either of those.
edit: DVDFab 6 doesn't seem to work very well for me at all. I suggest keeping version 5. Here is a link to version 184.108.40.206.