I figured something out the hard way. I occasionally only use half of an avocado. The problem with leaving the other half exposed is that it'll turn brown. If left overnight, it'll develop a rather unpleasant, leathery skin. Not so good.
I found that I can avoid this reaction by placing the avocado's cut side onto a flat plate. If you really want a good seal to prevent oxygen from certain avocado demise, a Cook's Illustrated tip suggested putting some oil on the plate before you place the avocado on it. But I find a flat plate is good enough.