The AM335X processor of the BBB provides three I2C buses:
I2C0
I2C1
I2C2
The BBB exposes the I2C1 and I2C2 buses via its P9 header, but the I2C0 bus is not easily accessible. I2C0 currently provides the communication channel between the BBB's processor and the HDMI framer chip of the built-in HDMI cape, so it should be considered unavailable for your use (unless you would like to void your warranty by soldering wires directly to the traces and chip pins on the BBB).
The I2C1 bus is available for your general use and is often the go to bus for I2C interfacing. If I2C1 is at its maximum capacity or unavailable, the I2C2 bus is also available for your use.
