Gamma-ray bursts (GRBs) remain one of the most inexplicable astrophysical phenomena observed today. While counterparts at other wavelengths would provide the best clues as to the nature of GRBs, none have been observed. To supplement studies on GRB distribution and population statistics, temporal morphologies, and spectral line searches, we focus on the analysis of GRB continuum spectral evolution. Previous spectral evolution studies have shown a variety of patterns: most individual pulses show a hard-to-soft evolution, but studies of both the SIGNE and BATSE GRB databases reveal several other patterns, including hardness-intensity tracking, soft-to-hard, static, and chaotic spectral evolution. This type of analysis attempts to identify spectral evolution signatures that can discriminate between different physical scenarios or different GRB subpopulations based on temporal profile, duration, intensity, or spatial distribution. Contrary to most studies that use only one model and one parameter to characterize spectral evolution, several models are used here. Statistically equivalent models are shown to give consistent physical results. I verify the variety of spectral evolution patterns present in GRBs, and investigate how the actual shape of the spectrum evolves, following multi-parameter spectral fits in time. Different spectral evolution patterns exist simultaneously in multiple parameters. Hardness-intensity correlations in pulse and over burst decay phases are quantitatively examined: correlation is often significant, but the relation between hardness and intensity is non-unique. Hardness-intensity lag-times are found to correlate to the rise-time of the hardness profile. Comparisons of double-pulse GRBs reveals a variety of results, including the implication that late-emitting pulses are less affected by early emission.