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.
Super-Earth
The discovery of Gliese 581e with a minimum mass of 1.9 Earth masses was announced on 21 April 2009. It was at the time the smallest extrasolar planet discovered around a normal star and the closest in mass to Earth. Being at an orbital distance of just 0.03 AU and orbiting its star in just 3.15 days, it is not in the habitable zone, and may have 100 times more tidal heating than Jupiter's volcanic satellite Io.