Music in India comes in two very different forms: Carnatic and Hindustani. Any discussion of Indian music must differentiate between these two forms.

Carnatic
The main percussion instrument in Carnatic music is the mridangam, which is a hollow jackwood barrel with pieces of skin stretched over the side (its actually much more complex, but it has its own node). Other common percussion instruments are the kanjira, which resembles a tambourine; the morsing, also known as a jew's harp; and the ghatam, an overturned clay pot.

Hindustani
The main and more or less only percussion instrument in Hindustani music is the tabla, which consists of two drums, one for each hand; both consist of a barrel with pieces of skin stretched over it. This is usd in almost all forms of classical Hindustani music. The mridangam is also used for a specific type of Hindustani performace called Dhrupad, which resembles Carnatic music.

There are also literally hundreds, perhaps thousands, of other folk and regional instruments; most are a variation on the instruments presented here.