How to center a graphic in its output cell

It is not very intuitive but you select the output cell and then select Format | Text Alignment | Align at Center. This will align the cells contents to centre as long as you do not delete the output cell. You can re-evaluate the expression and the output will stay centred.

You can also use Pane/Framed etc. + Full width + Alignment:

Pane[
 Graphics @ Disk[],
 Full, 
 Alignment -> Center
]

related: 46028

To get programmatically the same effect that Edmund points out, one can explicitly construct the output cell:

CellPrint[
 ExpressionCell[
  Plot[Sin[x], {x, -7, 7}],
  "Output",
  TextAlignment -> Center
  ]
 ]