We select E+A candidates from a spectroscopic dataset of ~800 field galaxies and measure the E+A fraction at 0.3<z<1 to be 2.7+/-1.1%, a value lower than that in galaxy clusters at comparable redshifts (11+/-3%). HST/WFPC2 imaging for five of our six E+As shows they have a heterogeneous parent population: these E+As span a range in half-light radius (0.8-8 kpc) and estimated internal velocity dispersion (50-220 km/s), and they include luminous systems (-21.6<M_Bz-5logh<-19.2). Despite their diversity in some aspects, the E+As share several common characteristics that indicate the E+A phase is an important link in the evolution of star-forming galaxies into passive systems: the E+As are uniformly redder than the blue, star-forming galaxies that make up the majority of the field, they are more likely to be bulge-dominated than the average field galaxy, and they tend to be morphologically irregular. We find E+As make up ~9% of the absorption line systems in this redshift range, and estimate that ~25% of passive galaxies in the local field had an E+A phase at z<1.