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How many earth-sized planets have been discovered outside our solar system? Is there a combined registry of them anywhere? Where might I look for more information?

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Nice quick resource: [exoplanet.eu][exoplanet.eu/catalog/]. Sort by mass, and you see three confirmed ones to date. Beware though - transiting planet masses often rely on density assumptions, and quoted RV masses (without transits) are always minimums that can be arbitrarily high depending on inclination. –  Chris White Jan 12 '13 at 20:39
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There are a couple of resources for you to look over the list of CONFIRMED extra-solar planets.

Wikipedia is always a nice starting point. Here is a list of the currently 53 known planetary SYSTEMS. And from that page, you can check out numerous other exoplanet details.

This article from August 2010 Space.com lists 5 candidates.

The definitive site though is http://exoplanet.eu/, which is touted as The Extrasolar Planets Encyclopaedia (The Interactive Catalog probably has the data you are looking for.). I would say that there are other sites as well, but this one is public and interactive. Many other sites require membership in the IAU for instance, and others don't seem to have been updated in a while. EDIT: Just found a nice table by The Planetary Society.

Since our ability to detect earthlike planets hasn't been that great until Kepler, and the results from Kepler are preliminary, maybe checking out the Released Kepler Planetary Candidates would be of value.

In perusing both of those sets of planets (555 confirmed, and the thousands of Kepler planets), I ran into quite a few that are earth SIZED although many of the tables are still sorted using Jupiter Mass as 1.0 (so you need to find planets near 0.00315 Mj).

Notice that I really stressed the word "confirmed" at the start. Right now we are still sifting through the data. And since we have a new method of reliably finding them (Kepler using the transit method), we have a lot of verification to still go through. Some specific exoplanets of interest as an answer to your question are listed on this Planetary Society Page. (Although I feel that The Planetary Society may be overstating some of the information about each of the planets.)

COROT-Exo-7 is only twice the mass of the Earth, and is the smallest exoplanet found as of early 2009. It was detected by the European planet-hunting spacecraft COROT, which uses transit photometry to search for terrestrial exoplanets. The planet orbits very close to its star and completes each revolution in a mere 20 hours. As a result, its surface temperature is approximately 1200 degrees Kelvin, enough to turn a rocky surface into molten lava.

Although, if you look at The Extrasolar Planets Encyclopaedia for COROT-Exo-7, you find points of data that don't fully support the statements by the Planetary Society. i.e. the mass of the planet is not known with certainty yet, ranging anywhere from 2.8 ± 1.4 MEarth to 6.9 ± 1.4 MEarth. So the following statements by the Planetary Society may be a bit more self serving, but still exciting.

Gliese 581c is one of the most Earth-like planet discovered to date. It is the third of four planets orbiting the red dwarf Gliese 581, 20.5 light years away, completing each orbit in a mere 13 days. Significantly, it is one of the smallest known exoplanets, measuring only 1.5 times the Earth's diameter and only 5 times its mass, and it is almost certainly a rocky world like our own. Even more suggestively it orbits close to the band around its star known as the "habitable zone," the only region where conditions are mild enough that water can exist in liquid form. Move closer to the star and all water will turn to vapor; move further away and water will turn to ice. But near the habitable zone water can remain liquid and life as we know it could potentially exist.

A small rocky planet with a mild climate where water can flow? Sounds a lot like our own world, and brings us one step closer to the discovery we are waiting for: another Earth, orbiting a distant Sun.

Gliese 581d is the outermost of the four known planets orbiting the red dwarf Gliese 581, 20.5 light years from earth. When first detected in 2007, Gliese was thought to have an orbital period of 82 days, placing it in an orbit just outside its star's "habitable zone" (HZ), where liquid water is stable. But additional observations over the next two years determined that the planet's true period is 67 days, which places it squarely at the heart of the HZ. With a minimum mass 7 times greater than the Earth, Gliese 581d is probably too massive to be a rocky planet like the Earth, and is more likely an icy world similar to Neptune. If this is the case, the planet might be completely covered by a deep ocean, making it the first serious candidate for a "water world."

Gliese 581e, is the lowest mass exoplanet discovered to date. Detected in 2009, it is the innermost of the four planets orbiting the red dwarf Gliese 581. With a minimum mass of only 1.9 "Earths" Gliese 581d is almost certainly a small rocky world like our own. But with an orbital period of just over 3 days, the planet is far too close to its star -- and therefore much too hot -- to sustain liquid water or life as we know it. The planet was discovered through the radial velocity technique, using HARPS spectrograph at the European Southern Observatory's 3.6 telescope at La Silla, Chile. It's discovery suggested that the radial velocity method, responsible for detecting the vast majority of known exoplanets. may prove sensitive enough to detect Earth-mass worlds orbiting in their star's habitable zone.

Overall, I would suggest The Extrasolar Planets Encyclopaedia as the more impartial source.

EDIT TO ADD: On the 20th of December (2011), NASA announced that there are more earth sized planets out there with the discovery of Kepler-20e and Kepler-20f. Keep in mind, as we start figuring out more and more about the universe, we'll be getting these type of announcements more frequently. I suggest you keep an eye on the Kepler Mission page as opposed to this answer, since they are more likely to be up to date. Note that this discovery adds a criteria to the significance of the planets. That is, they are earth sized AND they orbit a sun-like star. Hence the excitement about them.

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+1 fascinating answer –  user230 Jun 12 '11 at 15:00
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Thank you, Larian, for this exemplary answer. –  Brian Hooper Jun 13 '11 at 11:38
    
I think this needs to be updated with all the recent discoveries? Heck, you even commented on the JREF thread: forums.randi.org/showthread.php?t=245965 –  Brightblades Jan 8 '13 at 15:53
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