Since gravity is three dimensional why planets are orbiting only in one plane around sun.
It is believed that the planets formed when a cloud of gas underwent gravitational collapse. Any small angular momentum that the cloud started out with has to be conserved, and since the cloud's moment of inertia becomes smaller, it spins faster. Also, the centrifugal force "throws out" the edges of the cloud and makes it more disc-like.
As vartec said, pluto is an exception:
which has lead to speculation that it was gravitationally captured by our solar system rather than formed with the rest of the planets.
The planets generally are traveling in a plane. The Sun's axis is tilted about 30 degrees to this plane. Pluto's orbit is roughly 17 degrees off of the Earth's orbit. Eris is 44 degrees. There is a distribution of smaller bodies at all inclinations.
I would probably say it has something to do with the gravity or rather fabric of space if you want. E.g. take a look of the shape of our galaxy:
Do you see the similarity?
How the galaxy resembles our solar system?
It's about the fact that after a while the biggest "rotators" like the Sun or biggest planets win and other "slower rotators" will adjust to their way of rotation.
After than they cannot change their rotation from left to right or stop. Other force like collision of other planet or asteroid etc. can cahnge the direction of rotation.
A lot of things are involved. And one of them is gravity too.
Btw. even strange things are pulsars: http://en.wikipedia.org/wiki/Pulsar
This next few lines are off topic just to take in consideration ;): *To tell you the truth the scientists have troubles to detect some meteorites because they are moving too fast etc. So, be very sceptical to all scientists who claim that nowadays science know how pulsars and galaxy works. And the "hypo-theories" changes all the time. Take e.g. how Big Bang was the coolest thing 15- 20 years ago, now it's overcome with multiverse and other things. Another example is Big Freeze (brrr, slow ;) or her majesty recollapsing Big Crunch - These were the hypothesis popular among most of the scientists not more than 2 years ago. Now it seems that our Universe will pop like a balloon when it will get older. Who is right? Hard to say but... ...keep trying ;)