As edited (see Mudworm's post below):
There are 893 in the book, 880 in the main text and 13 in Appendix A, "Routes Too Late" (actually there are 14 in Appendix A, but of these, one was reported very differently - and went in - as two routes, but it is only one).
Since the book I've become aware of another 8, both in "found" routes and those newly established. Therefore I know of 901 routes exactly at this point.
Of the 8 that aren't in the book, two are 5.11 (although Jim McC says Flue Fire is hard 5.10, he's flat wrong). I didn't count the number of 5.11s that are actually in the book because that means I'd have to get up out of my chair and walk across the room, and since on Monday I'll be 48 years old, that's just too much to ask of me.