As a 5th grader, I learned that our Solar System comprised nine planets viz. Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune and Pluto.
This classification lasted until recently...and goodbye, Pluto...
On 24 August 2006, an assembly of the International Astronomical Union (IAU) in Prague, Czech Republic, (involving 424 astronomers), voted to remove Pluto's planetary status. Henceforth, it is classified as a "dwarf planet". Our Solar System now officially comprises
eight major planets.
According to a new definition, a full-fledged/classical planet is an object that orbits the sun and is large enough to have become round due to the force of its own gravity. In addition, a planet has to dominate the neighborhood around its orbit.
Pluto has been demoted because it does not dominate its neighborhood. Charon, its large "moon," is only about half the size of Pluto, while all the true planets are far larger than their moons. In addition, bodies that dominate their neighborhoods, "sweep up" asteroids, comets, and other debris, clearing a path along their orbits. By contrast, Pluto's orbit is eccentric and crosses the path of Neptune and also takes it well above and below the main plane of the solar system.
First discovered in 1930 by Clyde Tombaugh (USA), Pluto was initially thought to be larger than it actually is (it is actually smaller than many moons in the Solar System)
Later research revealed objects that rivalled Pluto in size, but were not classified as planets.
The decision, which was not without controversy, establishes three main categories of objects in our solar system:
Planets:
The eight worlds starting with Mercury and moving out to Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune.
Dwarf planets:
Pluto and any other round object that "has not cleared the neighborhood around its orbit, and is not a satellite."
Small solar system bodies:
All other objects orbiting the sun (such as comets and asteroids).
Here's a lineup showing the proposed 12 planet system, with a wedge of the sun at far left. Ceres, Pluto, Charon and 2003 UB313 are barely visible. Now Charon will continue to be considered Pluto's satellite, and the three other worlds will be dubbed "dwarf planets" rather than full-fledged planets. Ceres will be reintroduced as a planet, albeit as a "dwarf planet". The planets are drawn to scale, but without correct relative distances.

Martin Kornmesser / IAU
Plutons: Pluto-like objects. The definition still remains unclear, and I think they are essentially "dwarf planets".
Pluto is the prototype for the new category of "Plutons", which include 2003 UB313.