In 1924 Pauli proposed a new quantum degree of freedom to resolve inconsistencies between observed molecular spectra and the developing theory of quantum mechanics. He formulated the Pauli exclusion principle, perhaps his most important work. Uhlenbeck and Goudsmit later identified this degree of freedom as electron spin.
In 1927, he introduced the Pauli matrices as a basis of spin operators, thus solving the nonrelativistic theory of spin. This work influenced Dirac in his discovery of the Dirac equation for the relativistic electron.
In 1931, he proposed the existence of a hitherto unobserved neutral particle to explain the continous spectrum of beta decay. In 1934, Fermi incorporated the particle, which he called a neutrino, into his theory of radioactive decay. The neutrino was first observed experimentally in 1959.
In 1945, he received the Nobel Prize in Physics for his "decisive contribution through his discovery in 1925 of a new law of Nature, the exclusion principle or Pauli principle."
Pauli was famously perfectionist. This extended not just to his own theories, but to others'. According to a story well known in the physics community, after his death in 1958 Pauli was granted an audience with God. Pauli asked God why the fine structure constant has the value 1/(137.036...). God nodded, went to a blackboard, and began scribbling equations furiously. Pauli watched Him with great satisfaction, but soon began shaking his head violently...