No one knows. At least a thousand, perhaps 2,000. More get started every month, and some stop running after a cohort or three. f6s is used by most of us, but I’ve been at events with 50 people running 50 programs where 30 use other platforms or just a Google Form. That plus it matters whether you want to count accelerator brands or programs. Is TechStars 1 accelerator or 22?
Then there is the lack of definition of “accelerator.” Do you count the one-week programs? The six month programs? The co-working spaces and university competitions branding themselves as accelerators? What about the “incubators” that are cohort-based, mentor-rich, and 12 weeks long?
In short, it's an unanswerable question. Or at least a question that has no clear and simple answer.