Up until now, most fan art was in the form of pictures, writing or video. With 3D printing a whole new type of fan art is emerging. To me, fan art is the ultimate form of flattery for a company or product. It shows that you have a dedicated community. Unfortunately, there are companies who do not get the concept of fan art — or do not see any value in it.
So is it allowed?
Fair Use under US copyright law protects creators of fan art to certain extend. Though copyright is not really applicable to 3D models, and 3D printed items, but trademarks and trade dress are. Fortunately, there also exists a fair use clause in US trademark law as well.
Fair use is handled on a case-by-case basis by the courts. There are 4 factors defined in US copyright law, but courts use them, as well, when fair use in other IP laws are evaluated. It comes down to, if the use of trademark and trade dress is confusing to others, and their use will deprive the owner of income. In other words, is there a fair chance that others would think that the company owning the trademark — or trade dress — is behind the use of the word or dress in that particular case, and do you make money of it.
A lot of community driven non commercial created products on sites like Shapeways and Thingiverse would fall under fair use, and even use of trade names is allowed. Just make sure that there is no confusion that the item is not created or endorsed by the original trademark owner. For instance, name your product “like <trademark>” or “inspired by <trademark>”. Stay away from well-known trade dress like Coca Cola bottles or company logos. You can reproduce those for your own use, but do not make them publicly available.
The problem with fan art from an industry-perspective is that 3D printing allows for unlimited perfect copies. There is a chance, it will hurt sales for instance in merchandising. It is the same discussion, when audio CDs were introduced enabling perfect digital copies.
In short, yes, you can make fan art. Just do not make it commercially available, and make sure that there is no confusion that it is not an official product from that company. Unfortunately, some companies have a low threshold, and will try to bully you with cease-and-desist letters. They use their legal power over individuals to protect themselves. Would you go to court and face the Disney/Apple/Warner Bros whoever legal team on your own? I would not.
Disclaimer: I am not a lawyer and my posts on intellectual property and law are based on my own understanding of the law.