In Brazil, the Northeast region, particularly the state of Pernambuco, is prone to extreme hydrological events, especially episodes of heavy rain and long periods of drought. This study examined the spatiotemporal variability of rainfall in Pernambuco and the occurrence of extreme rainfall events. In this study, the following climate indices were used in daily rainfall data from the historical series from 1990 to 2020: (a) the Precipitation Concentration Index (PCI), (b) the Standardized Precipitation Index (SPI), (c) the Precipitation Concentration Degree (PCD), (d) the Precipitation Concentration Period (PCP), and (e) the Rainfall Anomaly Index (RAI), and the non-parametric Mann–Kendall and Sen’s slope tests, for the analysis of trends in the series of precipitation and the studied climate indices. The results obtained indicated that the east of the state presents more distributed precipitation throughout the year, being “moderately seasonal” in the mesoregions Metropolitana do Recife and Zona da Mata; “seasonal” in the Agreste Pernambucano mesoregion; and “strongly seasonal” in the Sertão Pernambucano and Sertão do São Francisco mesoregions. The SPI found that the most severe and extreme droughts occurred in almost all mesoregions during the 1990s, except in the Sertão do São Francisco mesoregion, where they were predominant in the 2010s. Furthermore, based on the RAI index, it was possible to have a greater occurrence of negative anomalies than positive anomalies, especially in the last decade (2010–2020), indicating a possible change in rainfall patterns. However, more in-depth research is required to determine the possible causes of this increased number of negative anomalies. Finally, the trend analysis indicated that only the SPI-12 presented trends in the Metropolitana do Recife, Agreste, and Sertão Pernambucano mesoregions. However, Sen’s slope test indicated that the magnitude of these trends is not significant.