I found this in the most recent issue of The Physics Teacher (September 2009). Surprisingly, there were several good articles in this issue. One article discusses a doable version of the Millikan Oil drop experiment. Maybe you are not a (or were not) a physics major, so you might not be familiar with how cool, but tedious and squinty the oil drop experiment can be.
In the Millikan Oil drop experiment, small electrically charged drops of oil are placed in a constant electric field. It turns out that a small enough number of electrons are on each drop so that the quantization of charge can be determined. Awesomely cool, but not very practical for an introductory physics lab. This can be done in an advanced physic lab.
The Physics Teacher article (The ‘Nut-Drop’ Experiment – Bringing Millikan’s Challenge to Introductory Students, L. McCAnn and E. Blodgett) shows a variation of the oil drop experiment that gets the same idea across. Instead of looking at the motion of a charged drop of oil, students will look at the motion of a container with different number of metal nuts in them (unknown number of nuts). Instead of finding the charge on one electron, the students will find the mass of a single nut.
The basic idea is that several containers will be filled with an unknown number of nuts and released in water. The terminal speed of the container (with nuts) in the water will be related to the number of nuts in the container. Students will then measure the terminal speed (they will need to determine the coefficient of drag for the container) for a bunch of different cases. They should see that the mass of the objects is quantized just like Millikan did with electric charge.
I will post more details after I set this up in lab. It should be appropriate for my intro mechanics lab after they do air resistance. I know they don’t normally study advanced topics like the oil-drop experiment, but this lab is really about forces.