EEG signal is an important source of information about real-time brain activity, useful both in medical diagnostic procedures and for brain-computer interface (BCI) construction. As a low signal-to-noise ratio and susceptibility to interference are an inherent feature of this biosignal type, careful preprocessing and artifact removal are very important in many practical applications. In this work, three different signal preprocessing approaches, including also methods for ocular and muscular artifact removal and signal interpolation, are compared on the basis of three EEG datasets defining various classification tasks (involving evoked and event-related potential detection and motor imagery). For each preprocessing method, we perform classification with a specialized convolutional neural network, presenting the obtained classification accuracy and measuring the extent of modifications introduced into the original signal by the preprocessing procedure. The obtained results indicate that no single artifact removal method is optimal for every possible type of classification task. Each case is analyzed in detail, which allows for drawing some interesting conclusions that may aid in selecting tools for EEG signal preprocessing and artifact removal in a range of BCI-related problems and challenges.