Are there any other planets besides the 8 known planets?

Answer 1

Yes, more than 700 planets are now known to orbit other stars, many in multiple-planet systems, and more are being discovered all the time. These are known as extra-solar planets or "exoplanets." Only the largest have been directly observed, but others have been inferred by orbital motion, spectroanalysis, and by their transits across their parent stars. The Kepler Mission is expected to soon begin announcing the discovery of planets as small as Earth that orbit relatively nearby stars. Kepler is focused on a narrow cone through the plane of our galaxy, and will be able to detect planets up to several thousand light years away. As of January 2012 Kepler has compiled 1235 candidate planets.

Within our own solar system the asteroid Ceres was considered to be a planet longer than Pluto was. Ceres, Pluto, Haumea, Makemake, and Eris are the five recognized dwarf planets in our solar system. Eris is actually larger than Pluto, but then, so is our moon.

It is very likely our galaxy contains billions of planets, but these are all we know for certain right now.

Legendary Planets

According to various legends, there was another planet closer to the sun than Mercury (Vulcan--proposed to account for discrepancies in Mercury's orbit later attributed to Einstein's General Relativity), and at least one farther away than Pluto. The likelihood is very small, however, that there is a planet of Mars' size or larger in trans-Neptunian space. The cometary realms such as the Kuiper Belt and Oort Cloud likely hold many dark, frozen planetoids of various sizes.
Within our own Solar System? Yes and no. Astronomers are still debating the exact definition of a "planet." Some astronomers say the ninth "planet," Pluto, shouldn't really count, as it's small, has an odd orbit, and orbits within a belt of debris out beyond the other planets called the Kuiper Belt. So if you go with that definition, there aren't even nine planets anymore - there are only eight. The International Astronomical Union, the official organisation that decides these things, decided to go with this view and took Pluto off their list of planets in 2006.

However, other astronomers believe that the word "planet" should be extended to include any round object orbiting the Sun. If you go by this definition, there are 13 currently known planets: Mercury, Venus, Earth, Mars, Ceres, Jupiter, Saturn, Uranus, Neptune, Pluto, Haumea, Makemake and Eris. And there are almost certainly more to come - when our telescopes improve and we're able to prove a lot of the more distant objects are round, that number could increase to dozens, even hundreds, over the next few years.

The "official" position the International Astronomical Union takes is that there are eight "planets" in the Solar System, and that everything smaller than that but that's still large enough to be round orbiting the Sun is a "dwarf planet." So there are currently eight planets and five dwarf planets, and probably many many more dwarf planets too. However, not all astronomers accept the IAU definition, so - eight or dozens, take your pick!

Beyond the Solar System of course there are probably billions and billions of planets orbiting other stars elsewhere in the Universe. In fact, astronomers recently found over 1200 of them in one go with the Kepler telescope - more than tripling the number known before! So however many planets you think there are in the Solar System, that pales in comparison to the number of planets we've already discovered elsewhere!

Answer 2

Yes, there are potentially thousands of exoplanets outside our solar system that have been discovered through various methods like the Kepler Space Telescope. These exoplanets vary in size, composition, and distance from their host stars.