We have conducted a search for giant pulses from four millisecond pulsars using the 100 m Green Bank Telescope. Coherently dedispersed time series from PSR J0218+4232 were found to contain giant pulses of very short intrinsic duration whose energies follow power-law statistics. The giant pulses are in phase with the two minima of the radio integrated pulse profile but are phase-aligned with the peaks of the X-ray profile. Historically, individual pulses more than 10-20 times the mean pulse energy have been deemed to be 'giant pulses.' As only 4 of the 155 pulses had energies greater than 10 times the mean pulse energy, we argue the emission mechanism responsible for giant pulses should instead be defined through: (1) intrinsic timescales of microsecond or nanosecond duration; (2) power-law energy statistics; and (3) emission occurring in narrow phase windows coincident with the phase windows of nonthermal X-ray emission. Four short-duration pulses with giant-pulse characteristics were also observed from PSR B1957+20. As the inferred magnetic fields at the light cylinders of the millisecond pulsars that emit giant pulses are all very high, this parameter has previously been considered to be an indicator of giant-pulse emissivity. However, the frequency of giant-pulse emission from PSR B1957+20 is significantly lower than for other millisecond pulsars that have similar magnetic fields at their light cylinders. This suggests that the inferred magnetic field at the light cylinder is a poor indicator of the rate of emission of giant pulses.