We present the results of a deep, serendipitous, long-slit spectroscopy-based survey for Ly alpha emission at high redshifts. The data were obtained over the course of 6.75 years at Palomar Observatory, using the Double Spectrograph and 4-Shooter instruments on the Hale 200 in. telescope. A total of 421 independent spectroscopic frames, covering an area of 14.97 arcmin(2), was surveyed over a 2500 Angstrom span from 5000 to 7500 Angstrom, with lesser areas surveyed across the entire optical passband. Out of 65 emission-line candidates found, we were able to determine firm redshifts for two quasars and 30 galaxies. An additional 20 galaxies have only tentative redshifts assigned, based on the identification of a single emission line as [O II]. The sample of galaxies with firm redshifts has a median redshift of 0.52, and reaches out to z similar to 1 The spectroscopic properties of these galaxies are consistent with the field galaxy populations identified in the deep spectroscopic surveys. No high-redshift tail is seen, consistent with the no-evolution models, though the majority of the data is not sensitive to [O II] beyond a redshift of 1. The remaining few objects are candidate Ly alpha galaxies at high redshift, with isolated, unidentified emission lines and little or no continuum. They require further spectroscopy to check on their nature. Assuming a Friedman cosmology with H-0=75 km s(-1) Mpc(-1) and Omega(0)=0.2, we have surveyed a rest-frame comoving volume of 20,400 Mpc(3) to a limit sufficient to detect unobscured star formation at a rate of 10M. yr(-1), and 102,600 Mpc(3) to a limit of 100M. yr(-1). These volumes surveyed are sufficient to contain of order 20 and 100 galaxies with L greater than or equal to L(*), respectively, assuming the local space density of spheroids and elliptical galaxies and no density evolution. These Limits are comparable to those achieved in narrow-band imaging surveys, while probing a different region of the relevant parameter space. The lack of detection of a population of Ly alpha-luminous objects could be due to dust quenching of the Ly alpha line, higher redshift of formation than surveyed, short lifetimes in the Ly alpha-bright phase, or even masking of the star-formation emission-line signature by an active nucleus.