How to add more polygons in edit mode How to add more polygons in edit mode without using any modifier or subdivision.
There are several approaches to 'add' more polygons

Subdividing

You can open the menu 'specials' by pressing W while beeing in edit-mode, where you can find 'Subdivide' and 'Subdivide Smooth'.

https://www.blender.org/manual/modeling/meshes/editing/subdividing/subdivide.html

Note: In the Toolbar (toggle with T) options will be displayed.

You can press Ctrl + R to cut edges. This will add more polygons.
https://www.blender.org/manual/modeling/meshes/editing/subdividing/loop_subdivide.html

Mesh adding

By pressing shift + A you can open up the mesh-menu, where you can select and insert a mesh.

Extruding

By pressing E you can extrude your selected vertices, edges or faces.

https://www.blender.org/manual/modeling/meshes/editing/duplicating/extrude.html

There are multiple extrude-modes that you can find pressing space and tiping 'extrude'. That will display all actions with 'extrude' in their name.

Insetting

By pressing I Takes the currently selected faces and creates an inset of them, with adjustable thickness and depth. If several faces are selected you can choose to inset them individually. 

https://www.blender.org/manual/modeling/meshes/editing/duplicating/inset.html?highlight=inset

Knife Tool

By pressing K you can open the 'Knife Tool' where you can cut faces, what will create more polygons.

https://www.blender.org/manual/modeling/meshes/editing/subdividing/knife_subdivide.html?highlight=knife

Joining

Although this can't be made in edit-mode. In Object mode select multiple meshes and join them pressing Ctrl + J