Gliese 876 System - Very nearby quadruple planet system and the first Red Dwarf found to have planets. The innermost planet (d) was the first found rocky planet around a normal star (the first true Super-Earth, at epistellar distances). The outer three planets c (Saturnian), b (Jovian), and e (Neptunian) are in 1:2:4 (30d/60d/120d) resonance (the exoplanet resonance and first triple-resonant planets discovered). The outermost planet has a Mercury-like orbit however it is very much colder than Mercury. Gliese 876 e actually receives only slightly more warmth from Gliese 876 than Jupiter does from our Sun. Planet b is second discovered by ELODIE after 51 Peg b and the second to have its mass exactly measured and the first to have done so by astrometry.
Gliese 674 System - The nearest red dwarf known to have a planet which is also the third nearest confirmed exoplanet to the Sun. The planet is a Hot Neptunian in a tight orbit that has a similar eccentricity to Mercury's.
Gliese 581 System - Small nearby Red Dwarf with six planets in tight circular orbits and a distant Kuiper belt where many comets orbit. Gliese 581 e was, at the time of its discovery, the smallest known dopplar-detected exoplanet and a super-Mercury, b is a hot-Neptunian, c is a super-Venus and the first detected in the habitable zone (initially heralded as habitable, but later thought too hot due to the greenhouse effect), g is a super-Earth and the first detected in the middle of the HZ (and is highly controversial, having many doubters and defenders), d is a super-Earth on the outer edge of the HZ which could support liquid water (due to its presumably large atmospheric pressure and carbon dioxide), and f (its existence is also highly controversial) is a cold super-Earth. Much further out, from 25 ± 12 AU to more than 60 AU, there is a cold debris disk reminiscent of the Kuiper belt but with 10 times more comets than the one in our solar system. The star is not very active.
Gliese 849 System - Contains the first long period exoplanet found around a red dwarf star using dopplar spectrometry. Also only the second Jupiter mass planet around a star less massive than half the Sun. Also the first confirmed Jupiter-sized planet at Neptune-like temperatures. There is evidense for a second planet.
Gliese 436 System - The second known red dwarf planetary system. Contains one of the first Neptunians discovered. Planet b temporarily later found to be the smallest exoplanet (about Uranus' diameter, though over 50% its mass) known to transit its host star and is currently the nearest (33 ly). Its temperature (712K) was measured to be higher than what it would be purely from radiation (520K), perhaps due to a greenhouse effect, somewhat higher than Venus. It was originally thought to have a layer of "hot ice", water solidified due to high pressures. It turned out that it was larger than thought and hot ice was not needed. It could still be a rocky super-Earth. It was later found to have a remarkably low levels of Methane and high levels of Carbon Monoxide for its 800K temperature. Possible explanations include Methane being changed into hydrocarbon polymers due to its star's ultraviolet radiation, CO being drafted upwards with winds, or observational defects. It's significant eccentricity suggests a possible neighboring planet. Planet c was announced to be the smallest known exoplanet (1.5 Earth's diameter), but was later retracted because variations in transit timing of the first planet did not occur and the proposed orbit would be unstable. It is still thought that a second planet of some kind is possible in the system.
OGLE-2005-BLG-390L System - Has first discovered Icy Super Earth, which was detected via Micro-lensing tens of thousands of light years away and was the smallest known exoplanet around a normal star at the time.
OGLE-2005-BLG-169L System - Contains the second discovered icy Super-Earth or Neptunian. This planet was detected via the Microlense technique.