Be stars are a class of rapidly rotating B stars with circumstellar disks that cause Balmer and other line emission. There are three possible reasons for the rapid rotation of Be stars: they may have been born as rapid rotators, spun up by binary mass transfer, or spun up during the main-sequence (MS) evolution of B stars. To test the various formation scenarios, we have conducted a photometric survey of 55 open clusters in the southern sky. Of these, five clusters are probably not physically associated groups and our results for two other clusters are not reliable, but we identify 52 definite Be stars and an additional 129 Be candidates in the remaining clusters. We use our results to examine the age and evolutionary dependence of the Be phenomenon. We find an overall increase in the fraction of Be stars with age until 100 Myr, and Be stars are most common among the brightest, most massive B-type stars above the zero-age main sequence (ZAMS). We show that a spin-up phase at the terminal-age main sequence (TAMS) cannot produce the observed distribution of Be stars, but up to 73% of the Be stars detected may have been spun-up by binary mass transfer. Most of the remaining Be stars were likely rapid rotators at birth. Previous studies have suggested that low metallicity and high cluster density may also favor Be star formation. Our results indicate a possible increase in the fraction of Be stars with increasing cluster distance from the Galactic center (in environments of decreasing metallicity). However, the trend is not significant and could be ruled out due to the intrinsic scatter in our data. We also find no relationship between the fraction of Be stars and cluster density. Subject headingg s: open clusters and associations: individual