I'm getting massive artifacts in Two Worlds. See the attached picture to see what I mean. Has any of you guys experienced the same and if so have you found a way to get rid of them?

Core i7 X-980 (6x3.3 GHz)
24 GB RAM
Radeon 5870 1GB RAM, Catalyst 10.7
Gigabyte X58A-UR3 motherboard
Windows 7 Ultimate 64-bit
By the way I just tried running Catalyst 10.6 instead. And the artifacts are still there. And I probably also should write that both processor and GPU are running at factory settings.

I know its unlikely with a game from 2007 on your rig, but have you checked to make sure the graphics card isn't overheating when you play the game and those artifacts show up?

Check DirectX (though I assume you would have done that).
Have you tried using the "Two Worlds control panel"? On your god of a machine you can easily push the graphics up a huge amount, the TW control panel makes this easy to do. It may also have a fortunate side effect of fixing your problem, though it's a bit of a long shot.
Other than that maybe try a reinstall? somewhere other than "program files" while running as an administrator, just to rule out problems due to UAC.

Thanks for the advice. But yes, I already have tried a reinstall and I put all my games in either D:\Games or E:\Games and I have disabled UAC a long time ago. I tried the control panel but I have found nothing to deal with the artifacts. I have found numerous mentions of the artifacts on other sites though no mention of solutions.

Did you check the temperature of your video card as suggested by Ralackk ?
The artifacts in the following thread were evidentally caused by a GPU running hot :
http://board.zuxxez.com/showthread.php?t=28892

Yes, the temperature of my card didn't go above 78 °C at any time. By the way I'm getting the same artifacts in Supreme Commander and Supreme Commander 2. But I haven't seen them in any other games.

Hmm what about your CPU temperature? Both the Supreme Commander games are pretty intense on the CPU, not sure about two worls but its worth checking real quick.

60-65 °C on the CPU

According to a post here, Catalyst Control Center has an inbuilt card testing feature so that might be worth running.
http://www.youtube.com/watch?v=SOgW-XZYusA&feature=related

As long as you didn't typo Celsius for those temperatures then that is hot. I have never used a core i7 but I can't imagine it is meant to be running so hot. My core 2 duo doesn't like running above 60c and starts to throttle itself at 57c I think.
The same goes for your video card. They can run hotter then cpu's but that is still very hot. You may want to look up optimal temperatures for that card.
As a suggestion, try running your computer completely opened up with a fan going on it. This should be done after letting the computer rest off for quite a while to let it cool. Then as soon as windows starts play one of the games that have these artifacts. This will give an indication whether it is heat problems ... though it may not be able to cool it down enough, in my experience this can take some computers down by 4-7c.

My computer crashed and I had to do a reinstall. And since then the artifacts have disappeared. I don't know what it was. They by the way also appeared in Supreme Commander (version 1, Forged Alliance and 2) and Race Driver Grid. And at least Grid is working fine now. i haven't tried any of the supreme commander games yet. So it seems everything's ok now.

I'm waiting for the eventual crash on my rig, as well. While I don't have quite as powerful a system as yours, I do have the i7 and a gig of video goodness, and my OS has been quite unhelpful, such as denying me installs from anything Bethesda has put out, and causing MassEffect to crash to desktop within seconds of startup.
I hope my re-install does the trick, as I don't see a reason yet to go from Vista to 7, unless I can get assurance that that would fix my problems. Two Worlds is the first game that has given my rig the ability to flex it's muscles.