How many pi bonds are there in a triple bond?

A chemical (covalent) bond is always made of one sigma bond. They then can have extra pi bonds around the central sigma bond, forming double or triple bonds.

A double bond will have a sigma and a pi bond: $1\sigma +1\pi$

A triple bond would have $1\sigma +2\pi$

A quadruple bond would have $1\sigma +3\pi$, and so on.