There are four main categories of classifications when determining the type of celestial body a object is. These classifications are: terrestrial planets (Mercury, Venus, Earth, and Mars), gas giants (Jupiter and Saturn), ice giants (Uranus and Neptune), and dwarf planets (Pluto, Eris, Haumea, and Makemake). Ceres at this current time is still labeled as an asteroid though it has many characteristics of a dwarf planet. There are three rules that are applied to determine whether a celestial body can be classified as a planet. These rules were determined by the International Astronomical Union (or IAU) and are as follows.
Is in orbit around a Sun.
Has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and
Has cleared the neighborhood around its orbit.
Here is a list of all the planets that fall within these rules according to the IAU.
Mercury — the closest to the sun and the second smallest planet in our solar system, Mercury has a rotation of only 88 days around the sun. Because of it's close proximity to the celestial giant, the surface of the planet reaches temperatures as high as 840°F during the day and hundreds of degrees below the freezing point at night. There is no atmosphere due to the intense temperatures so the planets surface is covered in pock marks and craters from meteor impacts.
Venus — this toxic planet, primarily consisting of carbon dioxide, is next in line from the sun and contains a pressure index that would crush anyone who landed on its surface. Though it is further away from the sun then Mercury, Venus is the hottest planet in the solar system and is able to be seen by the naked eye from Earth. A thick cloud shrouds the planet making it difficult to see its surface which attributes to its brilliance.
Earth — is the planet in which we live on and is the 3rd planet from the sun. Also known as "Terra" the Earth is the only planet within our solar system that is capable of sustaining advanced lifeforms, such as humans. The Earth's rotation around the sun is approximately 365 days and it is believed that the Earth is approximately four thousand million years.
Mars — the fourth planet from the sun the "red planet", so named for its reddish color due to the high iron content in its soil, has a rotation around the sun of 686 days. It's thin atmosphere, consisting primarily of carbon dioxide, makes it unsuitable for sustaining life but is believed to have at one time been capable of it and might still be able in the future.
Jupiter — the largest planet in our system, the mysteries of Jupiter has fascinated astronomers and non-astronomers alike for centuries. Poisonous gases completely cover its surface hiding what lies beneath and violent storms prevent any landings of probes onto the giant planet. Jupiter's atmosphere has been determined to be similar to that of the sun containing elements of hydrogen and helium.
Saturn — first viewed via telescope in 1610 by Galileo Galilei, is the 6th planet in our solar system from the sun. Like Jupiter, it's atmosphere is composed primarily of helium and hydrogen and it is the only planet discovered so far that has a lower density then water, approximately 30% lower. It is surrounded by a set of 9 whole rings and 3 broken rings that are comprised mainly of ice, rock, and space "dust".
Uranus — also known as the "sideways planet" because of its awkward rotation, is the 7th planet in our solar system from the sun. Its North and South poles are located where other planets equators are given to its strange rotation and it's 20 year long seasons. The level of methane gases in its atmosphere account for its blueish color but the main elements in Uranus' atmosphere is helium and hydrogen.
Neptune — is known as the windiest planet in our solar system and 8th furthermost known "planet" from our sun. It has a revolution around the sun of 165 Earth years. Like Uranus, Neptune has high traces of methane in its atmosphere contributing to its blue color. It is believe there is a second "unknown" element, though, that makes it a much brighter blue then Uranus.
Dwarf Planets are smaller in mass to their bigger "brothers" but still hold some qualifications to list them as planets rather than as just celestial objects such as asteroids and meteors. There are currently 4 planets in this category, all of which are currently located in the Kuiper Belt. These planets are Pluto, Eris, Haumea, and Makemake. These rules to determine the classification of a dwarf planet are as follows:
Is in orbit around the Sun,
Has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape2,
Has not cleared the neighborhood around its orbit, and
Pluto — at one time known as the 9th planet in our solar system, due to the new astronomy rules Pluto is no longer considered a planet but is now a "dwarf" planet. Located beyond Neptune in the Kuiper Belt (ring of bodies past Neptune), Pluto is smaller then our own moon and reaches temperatures of -387°F (-233°C).
Haumea — because of it's distance, little is truly known about Haumea other then its odd elongated shape and it is roughly the same size as Pluto. It's orbit path around the sun takes 285 Earth years and it is make of rock with a icy coating over the surface. This coating causes the dwarf planet to appear bright similar to the effect of sunlight on snow on Earth.
Makemake — is a recently discovered, March of 2005, dwarf planet located in the Kuiper Belt. Slightly smaller then Pluto, Makemake's surface consist of primarily frozen nitrogen, ethane, and methane. Makemake's orbital path around the sun is approximately 310 Earth years and it, along with Eris, is responsible for the new classifications of what constitutes as a planet.
Eris — the next "dwarf" planet with in the Kuiper Belt is Eris and has the most extreme orbital path that extends well outside of our solar system. It is believed that its surface temperatures vary's from -359°F (-217°C) to -405°F (-243°C). It's surface is covered in ice but as it comes closer to the sun and the ice melts, it's surface is closely similar to Pluto's.
Up In The Air Classification
These "objects" are currently under scrutiny as to whether they can be classified as a planet or as "Small Solar System Bodies". Currently there is only one body in our solar system that falls under this classification, Ceres.
Ceres — upon its first discovery in January of 1801 it was believed to be a comet then it was determined to be the missing planet between Mars and Jupiter. However, it is nested in a asteroid belt (the largest in our solar system) and so it was reclassified to be an asteroid. It is now considered as a "dwarf" planet but is still labeled as an asteroid, because in reality like Pluto, they have no idea how to truly classify this mysterious object.
These planets have yet to be physically discovered but are hypothesized based on scientific calculations as to exist. They may exist beyond our range of view or are hidden by other objects. Currently there is only one "possible" planet listed in this area which has been named Planet X or Planet Nine.
Planet X — according to Caltech researchers, there is a strong possibility that there is another planet in the far reaches of our solar system Planet X. Nicknamed "Planet Nine", there is no direct evidence that the planet exist, but there are several mathematical models and computer simulations that point to its existence. It is believed that the planet may be larger then Neptune and have an rotation of 10 - 20 thousand Earth years around the sun.