Electroencephalography (EEG) underpins neuroscience, clinical neurophysiology, and brain-computer interfaces (BCIs), yet pronounced inter- and intra-subject variability limits reliability, reproducibility, and translation. This systematic review studies that quantified or modeled EEG variability across resting-state, event-related potentials (ERPs), and task-related/BCI paradigms (including motor imagery and SSVEP) in healthy and clinical cohorts. Across paradigms, inter-subject differences are typically larger than within-subject fluctuations, but both affect inference and model generalization. Stability is feature-dependent: alpha-band measures and individual alpha peak frequency are often relatively reliable, whereas higher-frequency and many connectivity-derived metrics show more heterogeneous reliability; ERP reliability varies by component, with P300 measures frequently showing moderate-to-good stability. We summarize major sources of variability (biological, state-related, technical, and analytical), review common quantification and modeling approaches (e.g., ICC, CV, SNR, generalizability theory, and multivariate/learning-based methods), and provide recommendations for study design, reporting, and harmonization. Overall, EEG variability should be treated as both a practical constraint to manage and a meaningful signal to leverage for precision neuroscience and robust neurotechnology.