The comments already solve the problem, in particular by using the File menu or Export. But there is also a way to get the usual behavior back that you expect for single Plot output, i.e., a contextual menu appearing when the graphic is selected. It just has to be selected in the "right way."
Create the plots, and then press the back arrow to bring the cursor right behind the graphics row out put:
{plt1, plt2, plt3} = Table[Plot[Sin[x + a], {x, 0, Pi}], {a, 0, 2}];
GraphicsRow[{plt1, plt2, plt3}]

The vertical line on the right is the cursor. Now press Shift + back arrow to select the graphic:

As you can see, the orange highlighting around the graphic appears, instead of a gray box. Now right click on the orange border (not the graphic because that will again switch to the gray box):

And there's the contextual menu you were looking for!
Edit
Another way of getting the orange box on whose border you want to right-click is this:
First click on the graphics row to get the gray box, then press Ctrl+. (the shortcut for Extend Selection) repeatedly until the whole output is highlighted in orange as in the above screen shot.
Rasterizeyour graphics and work with the result... – Yves Klett Jan 17 at 14:29Export["thePlotsThicken.png", GraphicsRow[{plt1, plt2, plt3}]]should work. Orplots = GraphicsRow[{plt1, plt2, plt3}]]followed by anExport. – cormullion Jan 17 at 15:35FullGraphicson the output, which should give you the context menu. Do note that it can throw a few surprises – rm -rf♦ Jan 17 at 18:58