Ionospheric disturbances, due to photoionization and energetic particle precipitation, occurring both on a regular recurring basis, and heightened due to space weather, impact global positioning, navigation, and timing services provided by Global Navigation Satellite Systems (GNSS). The development of operational services to mitigate the risks to users requires knowledge of how space weather impacts critical systems, and the frequency and magnitude of ionospheric disturbances including extreme events. Analysis of the largest values of total electron content (TEC) is important for the assessment of space weather hazards for systems sensitive to ionospheric effects on radio wave propagation and for the development of risk mitigation strategies. In this study, twenty years of global TEC maps are analyzed to determine the global distribution of the daily maximum TEC. Maximum TEC is shown to reach magnitudes of about 200 TECU in extreme cases, with the largest TEC normally observed at equatorial latitudes. A generalized extreme value distribution has been applied to the daily global maximum TEC and for the high (60 degrees-90 degrees; -90 degrees to -60 degrees), mid (30 degrees-60 degrees; -60 degrees to -30 degrees), and low-latitude (0 degrees-30 degrees; -30 degrees-0 degrees) regions in geographic latitudes to determine the 1-in-44 year (4 solar cycles) and 1-in-100 year maximum TEC with a 95% confidence interval. Additionally, the return period for TEC thresholds defined for safe operation by the International Civil Aviation Organization are discussed. Extreme values provide criteria for the development of operational systems and vulnerability assessment of critical systems dependant on GNSS.