Here's a fun set of experiments to do with kids. You need two pennies, two nickels and a voltmeter that can show voltages of the order of 10-50 millivolts. I used this cheap one. Probes with alligator clips make the experiments easier (I bought some alligator clips in Walmart's automotive section and soldered them on probes from an old multimeter), but you can do it with straight probes, too (in that case, replace "attach the probes" should be replaced with "touch the probes").
Experiment 1: Attach the probes to a penny and a nickel, respectively. Set the voltmeter to a scale that will show things of the order 10-50 mV (I used a 2000 mV scale). Have a volunteer hold the penny in one hand and nickel in the other. Measure the voltage. Ideally, the probes should be touching the coins, not the hands. I was getting about 15-35 mV, depending on which kid was holding the coins. If you're not getting much, maybe moisten the volunteers' hands. Then vary the coin combinations.
Experiment 2: Attach the probes to a penny and a nickel, respectively. Get two volunteers, and have each hold one of the coins. Make sure the volunteers aren't touching. Measure the voltage. Should be zero or very low (if the floor is conducting a bit). Now have them hold hands. There should be a very gratifying jump in voltage from this hand-holding switch! Note the voltage (it may take a while for it to stabilize).
Experiment 3: Set it up like for Experiment 2, but instead of having the volunteers hold hands, have the volunteer who is holding the penny hold out the other hand, palm up and outstretched. Put a nickel and a penny on that palm, with the nickel above, in such a way that the penny doesn't touch the skin (so don't put them in the middle of the palm, but maybe more on the heel; or maybe use a quarter instead of the nickel). Then instead of having the volunteers hold hands, have the second volunteer--the one holding the nickel--press a thumb from the free hand onto the penny that is on top of the nickel, being careful to make sure the penny doesn't make contact with the first volunteer's skin. Compare the voltage to that in Experiments 1 and 2. You've now got a two-cell human battery!
There are lots of fun variables to vary. Change the size of the volunteers. Wet or dry hands. See if drinking a lot makes a difference. See if temperature makes a difference (indoor vs. outdoor, say).
You can also do this, which I haven't tried, but it should work. What I did try, though, was this (though I used lime juice), which very gratifyingly powered an LED. When it went out, adding more lime juice turned it back on.