According to a recent infographic posted by the Scotch Whisky Association, there are 68 whisky distillery visitor centres open to the public:
I’ve been to a, current total, of 68 Scotch whisky distilleries, but not all of them (thinking Knockdhu, amongst others, have a visitor centre). Tours at these distilleries need to be prebooked.
Visiting distilleries has never been more popular than it is now and , even from 2012, tours are getting better and more consistently better year after year.