Kepler
This NASA mission is specifically designed to survey a nearby region of our Milky Way galaxy -- monitoring over 150,000 stars -- to discover Earth-size planets in or near the habitable zone of those stars and arrive at an estimate of how many of the billions of stars in our galaxy have such planets. As of January 2013, the number of planet candidates discovered in the Kepler data totals 2,740 potential planets orbiting 2,036 stars; 105 extrasolar planets have been confirmed.
Spitzer Space Telescope
This Earth-orbiting telescope is a premier tool in the quest to characterize exoplanets and the protoplanetary disks where planets are formed. Spitzer uses infrared technology to provide a unique view of the universe and allow astronomers to peer into regions of space which are hidden from optical telescopes.
Hubble Space Telescope
This Earth-orbiting telescope has been an important tool for planet hunters. The telescope has been used to look for the telltale wobbles of stars that indicate the presence of planets as well as the dimming of stars that occur when their planets pass in front of them.
Keck Interferometer
This ground-based observatory combines the light of the world's largest optical telescopes to measure the emission from dust orbiting nearby stars and to directly detect and characterize hot gas giant planets in other solar systems. The Keck Observatory also makes extremely accurate measurements of the spectra of stars -- breaking starlight into component colors enabling determination of many star characteristics that are critical in planet-finding: mass, size, age, and oscillating movements of the star towards or away from us, caused by graviational tugs from orbiting planets.
Convection Rotation and Planetary Transits Mission
The European Space Agency's Convection Rotation and Planetary Transits (CoRoT) mission is designed to observe planetary transits in front of their host stars. CoRoT's extremely sensitive light-detecting instruments can measure tiny dips in the brightness of a star that indicate the passage of a planet. Since its launch in December 2006, CoRoT has found 26 confirmed extrasolar planets. The number of possible extrasolar planets detected by CoRoT is even larger: 401 possible planet candidates detected with the telescope are in the process of being confirmed.