We have observed 1.7 × 106 individual pulses from the millisecond pulsar PSR B1937+21. About one pulse in 10,000 has more than 20 times the mean "pulse-on" flux density, and individual pulses as large as 300 times the average were observed. Comparable behavior has previously been observed only for the Crab pulsar. Giant pulses from PSR B1937+21 are seen in both the main pulse and interpulse components, and their amplitude distribution has roughly a power-law shape. Strong pulses differ greatly from the average emission: they are narrower, systematically delayed by some 40-50 μs, and many are nearly 100% circularly polarized. In addition to their potential importance for elucidating the physics of the emission region, the giant pulses may be useful for high precision timing measurements.