NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. This thesis consists of several surveys to search for binary stars and to estimate the frequencies of binary populations in globular clusters. The motivations for these searches are that 1) binary populations (even with a fraction as small as 3%) dominate the dynamical evolution of a globular cluster by producing a tremendous amount of energy through stellar encounters; 2) binary stars provide important information for understanding several apparently different phenomena such as blue stragglers, millisecond pulsars and X-ray sources. Two different techniques were employed in our surveys. The first survey is based on radial velocities obtained using the Norris Multi-fiber Spectrograph on the Palomar 200 inch telescope. We discovered 5 spectroscopic binary candidates among a total of 65 stars in the globular cluster NGC 5053. A total of 223 velocities were obtained for these 65 stars over a timespan of 3 years with a typical velocity error per measurement of 3 kms[...]. With detailed computer simulations we calculated the fraction of binaries which might have been missed in our detection sample due to unfavourable binary orbital configurations. Thus, we derived a binary frequency of 19-26% depending on the adopted period distribution function and orbital eccentricities. The second part of this thesis utilized a different technique -- the analysis of time series photometry. This method is efficient in searching for eclipsing binaries with periods of a few days, as demonstrated in our surveys in the two globular clusters M 71 and M 5. We discovered a total of 11 eclipsing binaries in the clusters, with periods of 0.3-0.7 days. All variables are main-sequence stars except one in M 5, which is a possible blue straggler. Their light curves indicate that one variable in M 71 and one in M 5 are detached or semi-detached eclipsing binaries; the rest of the 11 systems are W UMa type contact binaries. Based on a simple model of the evolution of contact binaries from initially detached short-period binaries, we estimated a lower limit of 1.3% on the frequency of primordial binaries in M 71 with initial orbital periods of 2.5-5 days. This implies that the primordial binary frequency is 22% assuming a flat logarithmic period distribution. This frequency is for binaries with initial periods shorter than 800 years since any longer-period binaries would have been disrupted over the lifetime of the cluster. A similar calculation was done in M 5. Adopting a flat logarithmic period distribution and a contact binary lifetime of 3 Gyr, we estimated an overall primordial binary frequency of [...]% for systems with periods of 2.5 days to 550 yrs. The discovery of 11 short-period main-sequence eclipsing binaries for the first time provides strong physical evidence which supports the scenario that some blue stragglers are formed by mass transfer and mergers in short-period main-sequence binary systems.