Question: I have an object with a high non manifold edge count. Is there a way to resolve them automatically or a way to make it easier to solve them manually?

Some of them are edges without a face and others are cubes connected to the object by one edge.
The object have a high polygon count because it is the result of various modifiers applied.

\_\_

Edit:

When I delete those edges they leave others "non manifold edges"
![enter image description here](https://i.stack.imgur.com/bAldR.png)
After deletion, the solid is open and some new non manifold edges are formed
![enter image description here](https://i.stack.imgur.com/RTIka.png)
Using make faces creates some non manifold vertices
![enter image description here](https://i.stack.imgur.com/GPQHA.png)

Answer: 
Re-topology is the best option, since it will generate a clean mesh for 3d printing and will consume less time then removing unwanted cubes, edges etc.

In given situation, I'll first delete half of my model and add a mirror modifier to it. covert my mesh to Quads and remove extraneous edges and vertices manually.

Use BSurface Addon for Re-topology, as it is the fastest method.
You can select all non-manifold edges/vertices by pressing `Ctrl` + `Alt` + `Shift` + `M`.

I don't know if this works for 3D printing, but you make it so *Select non-manifold edges* does not select those edges by making them separate:

![enter image description here](https://i.stack.imgur.com/qWa8k.png)

So the cubes are separate, but those edges are in the same place. (one vert is move to the side in the image so you can see they are separate)

Another way you could try is the [3D print toolbox addon](http://wiki.blender.org/index.php/Extensions:2.6/Py/Scripts/Modeling/PrintToolbox) ([introduced in 2.67](http://wiki.blender.org/index.php/Dev:Ref/Release_Notes/2.67/Print_Tools)), which has tools designed to help clean up meshes for 3D printing.