I've never really had a problem with vibrations affecting the computer in my car.. but I avoid pot holes and go really slow through rough roads, speed bumps, etc...
Now, with that point made, I wouldn't go offroading with a harddrive running either.. My hard drive is mounted on its side and hasn't had any problems with data errors or skipping or anything like that.. Mounting on it's side is probably the best bet because it pretty much eliminates the platters touching in a really brutal jar (and it would have to be REALLY bad)..
If you are really nervous, suspend the hard drive in some sort of caddy with rubber bands or strapping.. This has been done by quite a few people and seems to be a pretty good solution if you have the room and ingenuity to to it. You also can't go wrong with foam or rubber gromits on the drive to absorb some of the shock.
The hard drive is the only thing I would worry about in my system, because its the only main mechanical component.. Everything else is solid state and shouldn't be a problem.