Tipping points (TPs) in Earth's climate system have been the subject of increasing interest and concern in recent years, given the risk that anthropogenic forcing could cause abrupt, potentially irreversible, climate transitions. Paleoclimate records are essential for identifying past TPs and for gaining a thorough understanding of the underlying nonlinearities and bifurcation mechanisms. However, the quality, resolution, and reliability of these records can vary, making it important to carefully select the ones that provide the most accurate representation of past climates. Moreover, as paleoclimate time series vary in their origin, time spans, and periodicities, an objective, automated methodology is crucial for identifying and comparing TPs. To address these challenges, we introduce the open-source PaleoJump database, which contains a collection of carefully selected, high-resolution records originating in ice cores, marine sediments, speleothems, terrestrial records, and lake sediments. These records describe climate variability on centennial, millennial and longer time scales and cover all the continents and ocean basins. We provide an overview of their spatial distribution and discuss the gaps in coverage. Our statistical methodology includes an augmented Kolmogorov-Smirnov test and Recurrence Quantification Analysis; it is applied here, for illustration purposes, to selected records in which abrupt transitions are automatically detected and the presence of potential tipping elements is investigated. These transitions are shown in the PaleoJump database along with other essential information about the records, including location, temporal scale and resolution, as well as temporal plots. This open-source database represents, therefore, a valuable resource for researchers investigating TPs in past climates.