It's supposed to do that, it's been doing that ever since the game was release. What I suspect your problem is is that it's happening too fast. The answer there is that Parallax (now Volition and Outrage) never anticipated computers would go above 100Mhz so never bothered to set up delays for the bobbing. Now, with 1000Mhz+ CPUs it's starting to become a problem. A possible solution is D1X which allows you to set a framerate cap but I feel uneasy about recommending something I was never able to get to work...

Quite right. It has been years since I've had it installed. Now that you've reminded me, I do remember the bobbing of the ship, just not anything like the scale I'm seeing now. Of course the last system I actually ran this on was either a DX4-100 or a Pentium 200; a far cry from the 2000 MHz machine I'm trying to run it on today.
 
Thanks for pointing me in the right direction.

Unfortunately I do not have a fix either except for trying the slowdown programs...which do not seem to work all that great under NT for games. Sigh. Another game that needs up[censored].

A bit late (I don't even know if you're still around to read it) but I only just came across this myself:
 
http://www.planetdescent.com/site/files/d1/patches/
 
D1X 1.42/1.43 work under Windows XP (and most likely 2k as well) and allow you to set a framerate cap thus slowing the bobbing (along with the rest of the game) down. 1.42 apparently has less bugs(!) than 1.43 so I suggest you try that first especially when, in my testing (I haven't tried 1.42 yet), 1.43 has a habit of randomly crashing to the desktop for no apparent reason.

Yes, I'm still around. Thanks for the information. I'll give it a try.