Great experiment: Grab a car battery, run leads from each pole of the battery and stick 'em in a bucket of water. Hydrogen bubbles off the negative lead, oxygen bubbles off the positive.
Pretty simple right? But wait. I understand that the leads introduce or remove electrons from nearby water molecules, and the result is the breaking of the molecule into its constituent bits, H & O. But why is it that only H comes off the negative and O comes off the positive? Presumably, I've just broken a molecule and H and O should BOTH be bubbling up from the same area. If I'm getting H off of one lead, where did the O that it was attached to go?