To supplant the excellent answers already supplied, There is no definitive 'number' of raags, as explained. A hundred or so have survived down the ages, and a fraction of those in the performing circuit. read more
There is no exact count of ragas which are there in Indian classical music. Once ustad Vilayat Khan saheb in Sawai Gandharva Music festival said before beginning his performance - "There are approximately about 4 lakh ragas in hindustani classical music. Many of them are repetitious but have different names. read more
There are two main classical music traditions, Hindustani (North Indian) and Carnatic (South Indian), and the concept of raga is shared by both. Raga are also found in Sikh traditions such as in Guru Granth Sahib, the primary scripture of Sikhism. read more