Pauli's exclusion principle

Two similar particles cannot exist in the same state; they cannot have both the same position and the same velocity, within the limits given by the uncertainty principle. 

The exclusion principle is crucial because it explains why matter particles do not collapse to a state of very high density under the influence of the forces produced by the particles of spin 0, 1, and 2: if the matter particles have very nearly the same positions, they must have different velocities, which means that they will not stay in the same position for long.