Switching both (in and out) off is easy: In the Option Inspector (under Format) choose "Global Preferences". Then go to:

Cell Options->CellLabels->Show Cell Labels

and untick the box.

I just noticed that you want to selectively suppress the Out without suppressing the In; that's more complicated.

M.

One approach is to create a new stylesheet...  or to edit the private stylesheet for the notebook.  

For an example of the latter, choose the Format>Edit Stylesheet menu item.
Then in the "Chooose a Style" dropdown menu choose "Output".  
Then select the cell bracket of the Output  that has been placed in the private stylesheet  and choose the Cell>ShowExpression menu item. 
In the displayed cell expression change it to

Then unselect the  Cell>ShowExpression menu item and close the private stylesheet.  

The result is that your Output cells will no longer have the Out cell lables.