This question came up in email. It's not one that geologists askwe're content to say "about a dozen major ones." But, my correspondent says, "The folks who write the standardized tests for our school district seem to think that the number of plates is an important fact." So you must have one right answer. I would object strenuously to this question because there are several right answers.
But then we get into the quibbles of schoolkids and teachers. "What about India?" they want to know. "I never heard of this Somali thing," they whine. Okay, to get to India (tenth-largest at 12 million) we have to include the Somali and Nazca plates. Because India, whatever its status as a plate, is important for reasons that are cultural and pedagogicalit's right in the middle of the map, and you can't teach about continental collisions or the Tibetan plateau without mentioning it. And those top-ten plates add up to more than 90 percent of the Earth, so that should end the discussion.
But now that we've given in so far, we can't stop. In for a penny, in for a pound, as they used to say. Three more important placesthe Philippines, Arabia and the Caribbeancome next, riding on their own little plates of 5.5, 5 and 3.3 million square kilometers respectively. But we can't stop at thirteen because only slightly smaller, at 2.9 million, is the Cocos plate, so that makes fourteen. The next-smallest (the Caroline microplate) is quite a bit smaller at 1.7 million, so I'm cutting things off at 14.
Unfortunately, the whiners have another complaint: "Those aren't all on the map." The canonical plate map that I and everyone else uses doesn't match the list of the plates and doesn't match the plates I've just recited. The best map I have doesn't point them all out. If anyone is reading this from the U.S. Geological Survey, would you please produce a new map?
Another thing is that all the maps insist that the tiny Juan de Fuca "plate," actually just a microplate, belongs on the map with its name carefully pointed out, even though it ranks twenty-second in size. That's for pedagogical reasons, too, stemming from the history of science. The Juan de Fuca plate is where seafloor spreading was first convincingly mapped in the late 1950s, and that old map of seafloor "magnetic stripes" is still pulling its weight in the classroom.
So please, teachers, don't make your students learn a number for the number of plates. There isn't just one. And geologists, if you haven't read Don Anderson's treatment of this question, see "How Many Plates?" which was published in the May 2002 Geology.

