From an article about a "Planet X"
http://www.final-frontier.ch/Nibiru
(snippets from the article, translated from German):

The two infos, "orbiting time 3600 years", the next appearance in the inner region of the solar system in the year 2012 are describing the orbit of the hypothetic planet pretty well. With the celestial laws it can be calculated that Nibiru is in average of about 235 AUs (astronomical units, 1AU=distance earth-sun) in a distance to the sun. If the point of the closest approximation to the sun is at about 1AU, then the orbit has an excentricity of 0.996, the farthest distance to the sun would be at 469 AUs. The orbit of Nibiru would be similar to a long-period comet.

Such an orbit is principally unstable, because every time this planet passes the big planets of the outer solar system there is a chance coming too close to them and being deflected by one of them, causing a collision or (more likely) to be slinged into interstellar space. Since it's origin 4.5 billion years ago Nibiru must have had 1.25 million orbits through the solar system- it's almost impossible that it hasn't come close to Jupiter and being deflected.

However, let's assume Nibiru miraculously made it. If it actually had a distance of only 20AUs now, Nibiru would be 500 times brighter than Pluto. Such a planet would be impossible to overlook- even a worldwide astronomer's conspiracy wouldn't help: Every amateur astronomer with an average supply could see the planet through a telescope.

This all is even more true if Nibiru would be much bigger than the earth. Sometimes it's said Nibiru is a "brown dwarf" (an object of 13 to 80 times the mass of Jupiter). Given the approximation timepoint of 2012, this object could be seen with the naked eye! Such a planet would have messed up the orbits of all other planets even with it's first passing through the solar system billions of years ago.

Conclusion: Such a "tenth Planet" is impossible, which is orbiting the sun since billions of years. Possible only would be a big comet, like Hale-Bopp (about 50-80 km diameter), which had been deflected to that orbit some ten thousands years ago.

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As well, there is a detailed refutation of Zecharia Sitchin's The 12th Planet:
http://www.skepdic.com/essays/sitchin.htm

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Spooky