I don't know what Maya you are using, but I've always used 2010. This is the workflow that we used for a small unity 3D game project:
Export all of the
animations in one scene as a .fbx. Be sure you just select the geometry (it
usually helps to have it all grouped, but if you can't for some reason that's
okay) and hit export selected.
These FBX export options should be checked:
Geometry:
Edge smoothing,
Tangents and Bi-normals
Animation:
Animation,
Bake Animations,
Bake Animations,
(range of animation),
step = 1
Deformed Models:
Deformed Models,
Skins,
Blend Shapes (if using these),
Curve Filters,
Resample as Euler Interpolation,
Input Connections,
Instances to Objects,
Referenced Containers Content (if using any references),
FBX File Format
Binary
FBX200900
When you bring this into Unity, set animation generation
to "store in root." If all of your
animation is in this one file (which it should be). The "split
animations" box should be checked and define the names and range of these in the
chart below. When you eventually create an animation blending script, drag
and drop it on the animation object within the player prefab, not the prefab
itself.