Yes, one bit of light can bounce off another bit of light, but not directly, and the effect is very rare. Light is made out of small quantum objects called photons. When you turn on a lamp, the light bulb begins creating and emitting trillions upon trillions of photons. Photons are in a class of quantum particles known as bosons. Bosons are special because many bosons can occupy the exact same quantum state at the same time. Light being made of bosons is what makes a laser beam possible. A laser beam is a collection of many photons all in the same quantum state. In contrast, particles that are not bosons cannot occupy the same state at the same time. This is one of the effects that keeps the atoms in an object from collapsing to a single point. The principle that dictates that non-bosons cannot be in the same state is called the Pauli Exclusion Principle. Non-bosons are also called fermions. The fact that bosons such as light can occupy the same state means that they don't get in each other's way.