Disclaimer: While I do work at Shapeways, I don't work in the areas of the company which deal directly with this sort of thing. This is all my own personal advice as an independent artist familiar with the issues involved in reusing the work of others, not actual legal advice or a statement of official company policy.
Every game's models are owned by their game's publishers/creators/artists/etc. There are certain factors which dictate whether you can sell a model from a game.
For games by Valve Software, there's good news: they have agreed to let Shapeways' users sell models based on their work. You can check out the thread in this forum about the Valve partnership
here, and there are a couple of good blog posts in Shapeways Magazine about it
here and
here. Part of this agreement is that Valve gets a percentage of earnings form your sales based on their work, which is really the main issue in such things; Valve of course is entitled to some of the profits when others are selling things which reuse their property and work, and the Valve + Shapeways partnership allows an easy way for everyone to manage all that business.
There are also
certain games published under free licenses (open source, GNU, Creative Commons, etc.) that are open to reuse of their work; if you want to print and sell something from those games, you
may be automatically allowed to do so in line with those free licenses. Check into those games' individual projects for more info on what licenses they are applying to their artwork, and how it applies to resale.
For other publishers, you will want to get that information from them directly. If you're interested in selling 3D prints from a game, your next step is to contact the company who makes it to find out what they'd think of you selling their work. Maybe post to their own user forums, or contact them directly through their own sites. Maybe they'll grant you permission, maybe they'll have some sort of intellectual-property licensing system that you can apply to be part of, maybe they will just say no, but either way
they are the only ones who can tell you what you are allowed to do with the artwork they own. You might even like to send them a link to Shapeways' Valve posts as an example; maybe they would be interested in working out a Shapeways partnership like that which would allow folks to easily reuse their games' work in their own creations here.
Best of luck!