Classification of clouds, cirrus, snow, shadows and clear sky areas is a crucial step in the pre-processing of optical remote sensing images and is a valuable input for their atmospheric correction. The Multi-Spectral Imager on board the Sentinel-2's of the Copernicus program offers optimized bands for this task and delivers unprecedented amounts of data regarding spatial sampling, global coverage, spectral coverage, and repetition rate. Efficient algorithms are needed to process, or possibly reprocess, those big amounts of data. Techniques based on top-of-atmosphere reflectance spectra for single-pixels without exploitation of external data or spatial context offer the largest potential for parallel data processing and highly optimized processing throughput. Such algorithms can be seen as a baseline for possible trade-offs in processing performance when the application of more sophisticated methods is discussed. We present several ready-to-use classification algorithms which are all based on a publicly available database of manually classified Sentinel-2A images. These algorithms are based on commonly used and newly developed machine learning techniques which drastically reduce the amount of time needed to update the algorithms when new images are added to the database. Several ready-to-use decision trees are presented which allow to correctly label about 91% of the spectra within a validation dataset. While decision trees are simple to implement and easy to understand, they offer only limited classification skill. It improves to 98% when the presented algorithm based on the classical Bayesian method is applied. This method has only recently been used for this task and shows excellent performance concerning classification skill and processing performance. A comparison of the presented algorithms with other commonly used techniques such as random forests, stochastic gradient descent, or support vector machines is also given. Especially random forests and support vector machines show similar classification skill as the classical Bayesian method.