There are no legal restrictions for using any of the file types that Blender natively imports or exports.
OBJ is open source are unpatented, so its use is not restricted in any way. The other model formats that Blender supports natively are similarly unrestricted.
This is an EXCELLENT question, and one that is asked by creators far too infrequently.
It's uncommon for file type usage to be restricted, though implementing (in code) certain codecs or algorithms can require licensing. Even patenting the codec or algorithm is uncommon because it only discourages your competitors from adopting it, if they have to pay licensing fees to implement in import and export script. You might be thinking of the MP3 codec that is patented by Fraunhofer IIS and Thomson. Even in that case, making a file of that type does not require a license, but being able to make a file does. This is why Audacity doesn't support MP3s natively. Audacity would have to pay a licensing fee (or some other royalty) for the ability to use implement those algorithms. Then they wouldn't be able to afford to release it for free, anymore.
The fact that Blender is free, means that they aren't paying any licensing fees, which means there aren't any licensed algorithms (assuming they're doing what they're supposed to be doing).