A couple of examples:
- Irrlicht 3d engine openly claims support for various Quake formats, among others
- Blender openly claims support for a multitude of model formats, including Quake's md2
- Assimp asset loading library openly claims support for Quake's models as well as others
You should be safe if you claim support for other product's asset formats. Directly claiming support for other game's data might be ok too, but the user could be in violation depending on the EULA and such - you yourself commented that many allow personal use, so check it for each one in your mind. Examples of open-source games that depend on the original data are Arx Libertatis and OpenMW.
Regarding implementation, I think the main issue is whether the file formats contain patented features in which case it would be illegal to implement in some countries. This is most frequently encountered in formats that attempt some kind of compression, such as audio/video files.