Yay, the IAU did the right thing and Pluto takes its rightful place as a dwarf planet!
Short version: Our solar system has 8 classic "planets" (Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune) and at least 3 but probably more "dwarf planets" (Ceres, Pluto, 2003 UB 313 a.k.a. "Xena", etc). "Planet" means (1) it orbits the sun (2) big enough to be round-ish and (3) dynamically dominates its orbit.
That actually skimps on exoplanets (that orbit other stars), where the common meaning is "non-fusing thing orbiting a star" instead of #1, but I can let that slide for now. Without #3 we'd have at least 12 and probably more like 30 "planets".
Susan actually found a recent kids' book for Caspian last year that only lists the 8 planets explicitly, calls out Pluto as "a large cometlike object in the Kuiper belt" (I'll let the TNO/Kuiper-belt distinction slide), but doesn't call it a planet.