From 1995 to 1999, daily monitoring of the radio emission from the Crab pulsar at the Green Bank and Jodrell Bank observatories revealed a series of six sudden rotational spin-ups or glitches, doubling the number of glitches observed for this pulsar since 1969. With these observations, the range of time intervals between significant Crab glitches has widened considerably, indicating that the occurrence of Crab glitches may be more random than previously thought. The new glitch amplitudes Δν/ν span an order of magnitude from 2×10-9 to 3×10-8. Except in one case, which we suggest may represent an ``aftershock'' event, the frequency jumps display an exponential recovery with a timescale of ~3 days for the smaller glitches and ~10 days for the largest (1996) glitch. In the largest event, a portion of the spin-up was resolved in time, as was previously reported for the 1989 glitch. A pronounced change in ν also occurs after each glitch and is correlated with the size of the initial frequency jump, although for some of the smaller glitches this appears to be a temporary effect. We discuss the properties of the ensemble of observed Crab glitches and compare them with the properties of Vela glitches, highlighting those differences that must be explained by evolutionary models.