Why do all pictures of the solar system show the planet's revolving around the sun in approximately the same plane? Could a planet travel around the sun 90 degrees to earth orbit?
They all go round in nearly the same plane because they were formed in a rotating disk of gas and dust, and as they built up into planets, maintained the same sort of motion as the rotation of the plane of the disk.
However, it is possible for objects to end up with different orbits, as a result of near encounters with other objects, particularly if the other objects are much more massive. As a result, asteroids and Kuiper Belt comets, although they mostly go round the same way as the planets, have a considerably wider range of angles. (See http://cseligman.com/text/sky/orbits.htm
for diagrams showing the orbits of the planets and asteroids as seen from above the plane of the general rotation, and as seen from the side; for asteroids there is a lot of vertical scattering, while all the planets save Pluto are in essentially the same "horizontal" plane on a diagram the size of the Solar System.) And for comets that are at very large distances from the Sun, gravitational interactions with passing stars can completely randomize their orbits, meaning that every number describing the orbit (size, shape, orbital orientation and such) can have any possible value. So for such comets there are many that do orbit at an angle of 90 degrees to the "normal" plane of the Solar System.
Now, whether such orbits can be stable is another matter. The planets, by all going round in the same direction, tend to maintain roughly constant distances between their orbits; but objects passing through the Solar System at a large angle could pass very close to one of the planets, and have their orbits completely changed as a result of such a close encounter.
So to summarize,
(1) the general rotation is in one plane because that's the way that things happened to start out, but
(2) only objects that never have close encounters with massive objects such as planets have to stay that way, so
(3) asteroids and Kuiper Belt comets tend to go round the same as the planets, but with much more variation in their orientations, and
(4) comets that are normally very far from the planets can end up with orbits at any angle; but
(5) having such orbits makes the chance of an orbit-changing encounter much higher than normal, so
(6) only objects that move around more or less in the original plane of the system can have orbits that are stable over very long periods of time.
I hope that this is complete and clear enough to fully answer your question; but if there is any part of it that you would like to have better explained, just let me know.