two options - first, try turning on merge in the view header in Edit mode so that vertices moved into the same position get merged. Might be able to just 'G'to grab without moving, and confirm, and get the vertices to merge if Removing Doubles is not good enough when increasing the range in the F6 operator panel. Second, maybe try using the Array Modifier to model with, with Merge enabled, and then apply the modifier in Object mode.

two options - first, try turning on AutoMerge Editing option in the 3d viewport header in Edit mode so that vertices moved into the same position get merged. Might be able to just to press G to grab without moving, confirm action with LMB, and get the vertices to merge if Removing Doubles is not merging good enough when increasing the threshold in the Last Operator panel (press F6 to open after operator execution). 

Second way can be to use the Array Modifier to model with Merge checkbox in modifier's options enabled, and then apply the modifier in Object mode.