In The Deadly Assassin, it is stated that the Master has already used up all 12 of his regenerations. In many of his subsequent pre-reboot appearances, including the 1996 film, obtaining a new set of regenerations is his primary goal.
In The Sound of Drums, it's revealed that in exchange for his help during the Time War, the Time Lords gave the Master a new body and a new set of regenerations. It's never stated how many regenerations he was given, how many he has used, or how many he has left. However, we know of four post-Time War incarnations (played by Derek Jacobi, John Simm, Michelle Gomez, and Sacha Dhawan), so assuming Jacobi's Master is a different incarnation to the 1996 Master, he must have regenerated at least four times.
Just to confuse things even more, the Master has twice cheated death by transferring his consciousness into another person's body (in The Keeper of Traken and the 1996 movie), and once refused to regenerate (in Last of the Time Lords) only to be resurrected by outside forces (in The End of Time). If you count those, then the Master has regenerated at least 19 times; if not, then the count is at least 16.