Despite landslides impact the society worldwide every day, landslide information is inhomogeneous and lacking. When landslides occur in remote areas or where the availability of optical images is rare due to cloud persistence, they might remain unknown, or unnoticed for long time, preventing studies and hampering civil protection operations. The unprecedented availability of SAR C-band images provided by the Sentinel-1 constellation offers the opportunity to propose new solutions to detect landslides events. In this work, we perform a systematic assessment of Sentinel-1 SAR C-band images acquired before and after known events. We present the results of a pilot study on 32 worldwide cases of rapid landslides entailing different types, sizes, slope expositions, as well as pre-existing land cover, triggering factors and climatic regimes. Results show that in about eighty-four percent of the cases, changes caused by landslides on SAR amplitudes are unambiguous, whereas only in about thirteen percent of the cases there is no evidence. On the other hand, the signal does not allow for a systematic use to produce inventories because only in 8 cases, a delineation of the landslide borders (i.e., mapping) can be manually attempted. In a few cases, cascade multi-hazard (e.g., floods caused by landslides) and evidences of extreme triggering factors (e.g., strong earthquakes or very rapid snow melting) were detected. The method promises to increase the availability of information on landslides at different spatial and temporal scales with benefits for event magnitude assessment during weather-related emergencies, model tuning, and landslide forecast model validation, in particular when accurate mapping is not required.