The planets are rarely seen directly, but are found due to a dip in the brightness of a star as a large planet crosses in front of it. When the dip in brightness happens at regular intervals, the conclusion is that it is a planet circling that star. The light of the star shining through that planet's atmosphere tells us, via spectroscopes, what that atmosphere is composed of. The sort of planet we have discovered most frequently is the type large enough and close enough to its sun to block off a noticeable amount of light. We have already found several thousand planets, and there are probably billions more. The ones we have found are all close to us, astronomically speaking.
In addition, there are a number of confirmed planets which dwarf Jupiter.
Chthonioan Planets: these planets are found very close to their stars. It is thought they used to be very large "super Jupiters" which, because of their close proximity to their stars, have had their atmospheres stripped away, leaving only a rocky or metallic core. This stripping away is called "hydrodynamic escape." It is what happened on our moon and on Mercury if they ever had atmospheres at all.
These are massive gas giants with about the same mass as Jupiter. They orbit close to a star so they have a high temperature, whereas our Jupiter is very cold. Their orbit radius ranges out to about 0.5 AU whereas Jupiter is at about 5 AU. Because they are close to their parent star they are easily discovered as they transit the star, dimming its light.
Hot Saturns or “Puffy Planets”:
The density of Saturn is less than the density of water. That is the same way with the "hot Saturns." Their density is out of proportion to their size. They are gas giants with a large radius, but that large radius appears to be the result of a combination of a close orbit to their stars along with intense internal heating making them "puff" or inflate the atmosphere of the planet. So far six of them have been discovered.
These exoplanets are called "hot Neptunes" because they have the approximate mass of Uranus or Neptune. They orbit close to their stars, usually closer than Earth is to our sun. It is suspected that there are a great number of them out there, yet to be discovered.
Astronomers have discovered planets somewhat larger and more massive than Neptune. One orbits a star 120 light-years from Earth. Neptune has a diameter 3.8 times that of Earth and a mass 17 times Earth's. The best example of a "Super Neptune" is named HAT-P-11b, and is 4.7 times the size of Earth and has 25 Earth masses. An illustration of this system is below.
Water Worlds or Ocean Planets:
These are planets which have a lot of water. The surface of these planets may have oceans of water hundreds of miles deep. If the planet is close enough to its star for the water to reach the boiling point, it could become supercritical. What this means is that the steam evaporating from the water would be, essentially, as thick as the water and would have an even greater dissolving power. If the water planet were farther away, and thus cooler, it might have a very thick water-based atmosphere, producing a strong greenhouse effect on the planet -- a hot, steamy planet. The smaller the ocean planet, the less the gravity, and so it is assumed that not only could the water evaporate more quickly, but that the oceans themselves would have very high waves.
Super Earth planets have masses higher than Earth's, but much less than gas giants such as Uranus or Neptune. These planets are sometimes referred to as gas dwarfs or mini-Neptunes. These planets range from 1.9 to 17 Earth masses, but have nothing to do with living conditions, only mass.
From Wikipedia: The first super-Earth around a main sequence star was discovered by a team under Eugenio Rivera in 2005. It orbits Gliese 876 and received the designation Gliese 876 d (two Jupiter-sized gas giants had previously been discovered in that system). It has an estimated mass of 7.5 Earth masses and a very short orbital period of just about 2 days. Due to the proximity of Gliese 876 d to its host star (a red dwarf), it may have a surface temperature of 430–650 kelvin and may support liquid water.
Considering the size of our galaxy and how little of it we have been able to explore, there may be many other planets out there the sizes of our planets. We have found "rogue planets" which appear to orbit in the galaxy independently of any star.
Are these planets or stars? If they shine at all, it is only in the infrared. They are too large to be a planet and too small to be a star.
April 2015, farthest exoplanet yet detected