I’m surprised at the number of people who haven’t seen this one, but then again, neither had I until I went to the Exploratorium (where they’ll stick anything in a microwave).

Put a bar of Ivory Soap (no substitutes!) on a paper towel in the middle of the microwave.  Press go.  About 2 minutes should do it.  Here’s what happens:

And this video will show you what it looks like when you take it out afterwards

What’s going on?  Well, the reason that Ivory Soap floats (try it) is that it’s puffed full of air (here’s some history of why that is).  There are tons of tiny bubbles whipped into it, sort of like when you make whipped cream.  It’s an emulsion of soap and air.  The bubbles of air have water vapor in it.  When you microwave it, that water vapor creates pressure on the air bubbles making them expand and puff up.  The air bubbles themselves expand as they heat since the volume of a gas increases with temperature (Charles’ Law).  And the soap softens, which allows the whole thing to expand into a big puffy pile.  And when you stop heating it?  The soap’s no longer soft, so it gets rigid and hard, but stays its expanded puffy self.  You can use it like soap now, though it’ll be a little weird!

Other brands of soap tend to just melt.

Here’s a nice explanation, as well as how to use this as a classroom lesson on density, from Steve Spangler Science.  And some more classroom suggestions from About.com.