Robert Millikan's 1909 oil drop experiment is an American classic. It won Millikan the 1923 Nobel Prize in Physics. It spawned Paul Allen Stokstad's COmpany, PASCO. It made a surprising appearance in David Goodstein's Mechanical Universe, despite electron charge being decidedly non-mechanical. It's a great episode in that it elucidates the nature of the process of science (while debunking the overly simplified but easily posterized "scientific method").
We do not conduct the experiment in my high school physics classes. But we do watch the episode of The Mechanical Universe. And we do a very dry-labbed worksheet, originated by my mentor at Ann Arbor Huron High, Walt Scheider: The Millikan Oil Drop Experiment.
But before we do any of that, we solve a related quantization puzzle. Lab groups are given a set of numbers that could have been obtained by measuring the mass of various numbers of identical balls in a container. From the numbers, students must determine the mass of a single ball and the mass of the container.
Once the students have done that, we measure the mass of actual containers of various numbers of drilled balls. I'm a huge fan of drilled balls—every physics classroom should be rich with drilled balls. We measure the masses down to the grams and students get good results.
[Hint: don't use fewer than three balls in the lightest set and vary the number of balls by 2 and or 3 (but not by 1) between sets.]
Here's the worksheet for that. Millikan Mystery.