Nobody knows. The Kuiper belt is vast and Oort cloud even vaster.

We do have some limits from the WISE survey - which pretty much rule out extra stars in our solar system. Particularly doesn't seem possible there's an unknown red dwarf out there. A brown dwarf is just about possible - but it would have to be very dark, dim and cold and getting on for half a light year away. More typical brown dwarfs would be spotted right out to ten light years away.

But planets are not ruled out at all. Especially terrestrial ones. There could be Earth or Mars sized planets as close as the outer edge of the Kuiper belt and we wouldn't spot them. And as the new planet X idea shows, could be Neptune sized ones at a distance of several times the distance of Pluto.

LIMITS FROM THE WISE SURVEY

The original paper for the WISE results implications for planets is here:

A SEARCH FOR A DISTANT COMPANION TO THE SUN WITH THE WIDE-FIELD INFRARED SURVEY EXPLORER

The survey is for gas giants, and stars rather than terrestrial planets shining only by reflected light. It was an automated computer search with any tricky borderline cases investigated by hand.

The scans overlapped at the ecliptic poles. Each spot of the sky was photographed twelve times in the ecliptic, but hundreds of times at the poles. So there is no way it can miss planets that are out of the ecliptic - it is more sensitive to those than planets in the ecliptic.

Artist's impression of the Wide Field Infrared Survey Explorer which has produced the tightest constraints to date on Planet X.

It gives strong constraints on a Jupiter or Saturn sized object. A Jupiter sized object must be at least 82,000 au from the sun, and a Saturn sized object at least 28, 000 au. But a brown dwarf can actually be similar in size to Jupiter and also very cold and as well as that, it can be much darker than Jupiter in appearance (though not invisible in reflected light, - our Moon is as dark as worn asphalt and of course, easy to see).

Anyway, apparently it would be possible for a small, dark and very cold five billion year old brown dwarf to be in our solar system at a distance of 26,000 au, even closer than the limit for an undiscovered "Saturn". Even so, that's 650 times the distance to Pluto, or 0.41 light years away - so far away it would take light over 21 weeks to get from the brown dwarf to Earth.

The survey could spot the more usual 150 K brown dwarf out to ten light years away. That's why the idea of an unseen star is getting increasingly unlikely. It couldn't have missed a red dwarf star, or any kind of a star at all. It just possibly could have missed a very dark brown dwarf in a Nemesis type orbit. But brown dwarfs are less common than they used to be thought to be. As a result of the WISE survey again, it's now thought that there are six normal stars for every brown dwarf.

(last part of this is an extract from my new science20 article: Why This New "Planet X" Is No Threat To Earth :).  )

BTW I think Planet Nine is a very silly name for it. Surely we can think of a better name, like Nemesis and Tyche were?

First, it depends how you define a planet. To those who think Pluto and Ceres should be called planets, then Neptune is planet 9, and Pluto planet 10, and then it would be planet 11.

It could even be planet 12 or 13 if we find other planets in between it and Neptune.

While if you adopt the IAU definition it is only very borderline a planet. It is almost exactly on the line between a planet and a non planet, just a bit edging towards "planethood". For the emprical definition it might take years or decades to be sure it is a planet.

I think there's at least a possibility that the definition of a planet may change again, a significant number are calling for it to be reconsidered (6,000 have signed the petition and several hundred asked for it to be reconsidered immediately after the decision was made) and then its name might have to change depending on how many planets are now counted between it and the sun.

And what other planet is named by a number? Should we call Earth "Planet 3" and Mercury "Planet 1" etc?

See also my  science20.com: Why This New "Planet X" Is No Threat To Earth :).