This is close to 2 years after the event but others may find it useful -
I've been exporting rigged mesh objects using a mix of .OBJ, and .FBX, but before you read on you might like to scan down to my latest edit where I simply "append" a complete scene in the model's original Blender file to the current project. This is incredibly simple and trouble free.
The original post follows...
The obj format exports mesh and materials/textures from and then back into another Blender project. The fbx exports the bones, their names, size/scaling and joints accurately, albeit with a bonus "extra" bone at the end of each chain. I just delete those. When they are both imported to the same cursor location, the mesh and bones match. What is needed after that is to remove animation keyframes in the dope sheet first, then redo their inverse kinematics constraints, re-parent the mesh to the parent bones and that's it! An accurate export/import to another project!
I use the copy/paste method when that's possible for a new scene/project, but sometimes a rigged model is added to an existing project, and that's when I use the above.
Your problem has probably been long been resolved, but other newbies might like to explore this method...
Latest Edit 13/9/2016:
Not to take away from MarcClintDion's excellent suggestion I've included my own 'evolutionary process here' as an alternative in case the use of extra instances of Blender don't quite go according to plan...
From within your current project, go to top left of 3D window and click on File -->Append.
Select the model's original Blender file. Several folders will list up. Select the one called "Scene".
From there select the scene required. Often there's only one.
You'll be brought back to your current project's 3D window. Go up top and expand the scene menu. You'll see the newly appended scene labelled as scene.001 or similar.
Select that and you'll be into a working copy of the model's Blender file. Select the entire model. The Z key will make it easier to select it all using the B (box) mode. Press CTL-C (copy).
Go back to your current project's scene and press CTL-V. (paste)
The model will be copied intact and with whatever attributes/animation etc it possessed before. If these aren't required it would be wise to eliminate them whilst still in the appended scene. You won't be cluttering up the current project's dope sheet etc that way.
You could as an alternative to appending an entire scene, select the model's folder instead and append that from the original file but with Newbies it could lead to confusion, and why I opt to append the entire scene. It's a simple matter to go back to the appended scene and re-copy the model(s) when things don't work out.
When you're done with the appended scene it can be deleted.
This makes porting models from one Blender file to another much less troublesome and easier than exporting then re-importing as objects.
I'll certainly be trying MarcClintDion's answer.