Pluto's 248-year long orbit is less circular - more elliptical or "egg-shaped" - than those of the other planets. Pluto's orbit has an eccentricity of 0.25, which means that Pluto's distance from the Sun is as little as 29.7 AU - temporarily bringing it closer to the Sun than Neptune - and as great as 49.7 AU.
For about 20 years in each orbit, Pluto is actually closer to the Sun than Neptune. While all of the other planets have orbits that are close to the ecliptic plane, Pluto's orbit is inclined by 17 degrees.
While Pluto's orbit is close to Neptune's, the planets won't collide since their orbits are in an exact resonance. Pluto orbits the Sun twice for every three orbits of Neptune. As a result, Pluto and Neptune are never very close to each other. This is strong evidence against the idea that Pluto is an escaped moon of Neptune.
Imagine an observer looking down on the solar system from 18 billion miles (30 billion kilometers) above and watching Pluto from the time of the U.S. Declaration of Independence in 1776 through historic events of the past couple of centuries. By the time the planned New Horizons mission makes its flyby of Pluto in 2015, the dwarf planet will have made almost a complete orbit of the Sun.
The period around Pluto's closest approach to the Sun - known as perihelion - was a busy time for Pluto events! Click the graphics below for a closer look.
These diagrams were made using data from the Jet Propulsion Laboratory's Solar System Simulator.
The diagrams below show the resonance of Neptune's and Pluto's orbits another way. The upper diagram looks down on the solar system from above the Sun. The lower diagram "fixes" Neptune and the Sun, following the planets' orbits over thousands of years. Check how Pluto's eccentric orbit maps out a strange, curly path — but never comes close to Neptune.
(Note: This comes from a chapter by Malhotra and Williams in the book Pluto and Charon, edited by Alan Stern and Dave Tholen.)