Regime shifts are large, abrupt and persistent critical transitions in the function and structure of systems. Yet it is largely unknown how these transitions will interact, whether the occurrence of one will increase the likelihood of another, or simply correlate at distant places. Here we explore two types of cascading effects: domino effects create one-way dependencies, while hidden feedbacks produce two-way interactions; and compare them with the control case of driver sharing which can induce correlations. Using 30 regime shifts described as networks, we show that 45% of the pair-wise combinations of regime shifts present at least one plausible structural interdependence. Driver sharing is more common in aquatic systems, while hidden feedbacks are more commonly found in terrestrial and Earth systems tipping points. The likelihood of cascading effects depends on cross-scale interactions, but differs for each cascading effect type. Regime shifts should not be studied in isolation: instead, methods and data collection should account for potential teleconnections.