Importing meshes into Unity can be achieved from two main types of files:
Exported 3D file formats, such as .FBX or .OBJ
Proprietary 3D application files, such as .Max and .Blend file formats from 3D Studio Max or Blender for example.
Either should enable you to get your meshes into Unity, but there are considerations as to which type you choose:
Exported 3D files
Unity can read .FBX, .dae (Collada), .3DS, .dxf and .obj files, FBX exporters can be found here and obj or Collada exporters can also be found for many applications
Advantages:
Only export the data you need
Verifiable data (re-import into 3D package before Unity)
Generally smaller files
Encourages modular approach - e.g different components for collision types or interactivity
Supports other 3D packages whose Proprietary formats we don’t have direct support for
Disadvantages:
Can be a slower pipeline for prototyping and iterations
Easier to lose track of versions between source(working file) and game data (exported FBX for example)
Proprietary 3D application files
Unity can also import, through conversion: Max, Maya, Blender, Cinema4D, Modo, Lightwave & Cheetah3D files, e.g. .MAX, .MB, .MA etc.
Advantages:
Quick iteration process (save the source file and Unity reimports)
Simple initially
Disadvantages:
A licensed copy of that software must be installed on all machines using the Unity project
Files can become bloated with unnecessary data
Big files can slow Unity updates
Less validation, so it is harder to troubleshoot problems