Planet
The smallest known planet is PSR B1257+12A, one of the first extrasolar planets discovered, which was found in 1992 in orbit around a pulsar. Its mass is roughly half that of the planet Mercury. The smallest known planet orbiting a main-sequence star other than the Sun is Kepler-37b, with a mass (and radius) slightly higher than that of the Moon.
Kepler-37b
To date, Kepler-37b is the smallest planet discovered around a main-sequence star outside the Solar System. Detection of Kepler-37b was possible due to its short orbital period, relative brightness, and low activity of its host star, allowing brightness data to average out quickly. The discovery of Kepler-37b has led Jack Lissauer, a scientist at NASA's Ames Research Center, to conjecture that "such little planets are common".