Planets and Dwarf Planets of the Solar System as of 2008.
Question: Why is Pluto not a planet anymore?
Answer: In 2006 the International Astronomical Union (IAU) decided that Pluto should no longer be called a planet. Instead we now refer to it as a "Dwarf Planet". This leaves eight planets in the Solar System: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune.
When Pluto was first discovered in 1930 it was thought to be alone in its orbit. Since then, astronomers have realised that Pluto sits amongst a band of many thousands of objects, known as the Kuiper Belt. Pluto is larger than almost all of these, but in most other respects is similar to them.
In 2005 an object (now called Eris) that is much larger than Pluto was discovered. This raised the question as to whether all objects larger than Pluto were planets, with the Solar System potentially having over a dozen planets, or whether to stop calling Pluto a planet. In the end, the IAU decided that an object that is large enough to be spherical, but sits in a band of similar objects, like Pluto in the Kuiper Belt, is called a "Dwarf Planet".
There are currently five known dwarf planets in the Solar System: Pluto; Eris and two others in the Kuiper belt, and Ceres, the largest object in the asteroid belt. More dwarf planets are likely to be discovered. However it is extremely unlikely that there will ever be a ninth planet found because any new worlds found will probably be part of the Kuiper Belt, or else they would have already been seen.
Pluto is not the only object to have been demoted like this. When it was first discovered in 1801, Ceres was thought of as a planet. However with the discovery of the Asteroid Belt, astronomers decided to stop calling it a planet.
In any case the most important scientific questions regarding Pluto and other objects like it do not depend on whether we call them planets or not. Pluto is still a very interesting and unknown world. Some of these questions will be addressed by New Horizons, the first space mission to Pluto, which will reach the Dwarf Planet in 2015 and then move on to explore other parts of the Kuiper Belt between 2016 and 2020.