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Name the images as descriptively as possible, e.g. small-red-widget.gif, and use "small red widget" in the alt tag.
It can only help. The only counterargument that I think would be valid is that longer file names are going to bulk up the size of your page as perceived by Google. Smaller pages do much better in Google than larger pages, everything else being equal.
Mind you, if you rename spacer.gif to be keyword1-keyword2.gif, I think that's a mistake.
As far as how to do it, I wouldn't do it manually. Build a spreadsheet (product name, oldgraphicname, newgraphic name) and then do the rename in one fell swoop with a DOS batch program or something similar.