Definitely took off right at the turn of the century.
My first several clumsy experiences early high school were mostly furry. Slowly that started to fade, and by about sophomore or junior year of college (about 2003ish) it had gotten to the point where it was incredibly rare to find a girl under 30 who wasn't clean-shaven.
If I had to mark a culturally significant landmark, it would be the foreign exchange student scene in American Pie. Where she says she's shaved and he loses it.
It seems like before that you almost never saw it (outside of porn, where even then it was kind of rare), and then "the movement" began almost immediately after.