I just found an index on the Wizards of the Coast website that has all of the prestige classes along with a quick description, and the product and page number they appear on. There are 782 of them. 700. And 82.
And that's just the official prestige classes. The third party prestige classes multiply that number exponentially. Heck, that doesn't even include classes from Dragon Magazine (unless they were subsequently reprinted in an official book, which did often happen.) It's also a bit overstated, as some classes were updated, appear in two products, and are subsequently listed twice. But still. Holy cow. I had no idea there were so many.
I tried to make a quick list of "base" classes; 1-20 level classes that appeared in official products, and I got 44. I'm not sure that's completely comprehensive, but it's gotta be pretty close. If anything, the number goes up a little, but I'd be surprised if it goes past 50.
Now I should count up playable races. I mean, with Savage Species almost every monster entry can be converted to a race, but I mean ones that have actually been seriously proposed as a playable race. I'm sure it's somewhere between 50-100, if not even more.
That, my friends, is a lot of options.