Unity supports FBX files which can be generated from many popular 3D applications. Use these guidelines to help ensure the best results.
Select > Prepare > Check Settings > Export > Verify > Import
Be aware of export scope e.g. meshes, cameras, lights, animation rigs, etc.
Prepare your assets:
Check the FBX export settings
Use the Latest Version of FBX where possible.
Autodesk update their FBX installer regularly and it can provide different results with different versions of their own software and other 3rd party 3D apps
See Advanced Options > FBX file format
If you have any issues you can revert to 2012.2 if necessary
Verify your export
See below for Maya FBX dialogue example: