We present the results of a large-scale analysis of event-related responses based on raw EEG data from 17 studies performed at six experimental sites associated with four different institutions. The analysis corpus represents 1,155 recordings containing approximately 7.8 million event instances acquired under several different experimental paradigms. Such large-scale analysis is predicated on consistent data organization and event annotation as well as an effective automated preprocessing pipeline to transform raw EEG into a form suitable for comparative analysis. A key component of this analysis is the annotation of study-specific event codes using a common vocabulary to describe relevant event features. We demonstrate that Hierarchical Event Descriptors (HED tags) capture statistically significant cognitive aspects of EEG events common across multiple recordings, subjects, studies, paradigms, headset configurations, and experimental sites. We use representational similarity analysis (RSA) to show that EEG responses annotated with the same cognitive aspect are significantly more similar than those that do not share that cognitive aspect. These RSA similarity results are supported by visualizations that exploit the non-linear similarities of these associations. We apply temporal overlap regression, reducing confounds caused by adjacent event instances, to extract time and time-frequency EEG features (regressed ERPs and ERSPs) that are comparable across studies and replicate findings from prior, individual studies. Likewise, we use second-level linear regression to separate effects of different cognitive aspects on these features across all studies. This work demonstrates that EEG mega-analysis (pooling of raw data across studies) can enable investigations of brain dynamics in a more generalized fashion than single studies afford. A companion paper complements this event-based analysis by addressing commonality of the time and frequency statistical properties of EEG across studies at the channel and dipole level.