My two favorite experiments:
Millikan Oil Drop Experiment: Measured the charge of an electron for the first time. Brilliant in design, and very very hard to execute correctly.
Michelson-Morley Experiment: Measured the speed of light so accurately that it proved that space is a vacuum. Invented the interferometer.
I also have a soft spot for the Penzias Wilson discovery of cosmic background radiation, but it's not really an experiment per se. I'd also add Alain Aspect's Bell Inequality experiment, but I really don't understand the experimental setup well enough.