[harshadwaj]

To put a specific number, in Carnatic Music there are 72 of them and are called 'Melakarta' ragas - https://en.wikipedia.org/wiki/Melakarta

[crazyphoton]

Only ~15 of them are popularly performed though. And the melakartas would form the minority of the ragas in a typical concert, although they often tend to be the centerpieces.