The detection of activities of daily living (ADL) and the detection of falls is of utmost importance for addressing the issue of serious injuries and death as a consequence of elderly people falling. Wearable sensors can provide a viable solution for monitoring people in danger of falls with minimal external involvement from health or care home workers. In this work, we recorded accelerometer data from 35 healthy individuals performing various ADLs, as well as falls. Spatial and frequency domain features were extracted and used for the training of machine learning models with the aim of distinguishing between fall and no fall events, as well as between falls and other ADLs. Supervised classification experiments demonstrated the efficiency of the proposed approach, achieving an F1-score of 98.41% for distinguishing between fall and no fall events, and an F1-score of 88.11% for distinguishing between various ADLs, including falls. Furthermore, the created dataset, named “ShimFall&ADL” will be publicly released to facilitate further research on the field.