Plotting growth curves is a powerful graphical approach used in exploratory data analysis for continuous longitudinal data. However, plotted growth curves for multiple participants rapidly become uninterpretable with categorical data. Categorical data define specific states (e.g., being single, married, divorced), and these states do not necessarily need to represent any hierarchical order. Thus, a trajectory becomes a sequence of states rather than a continuum. We introduce a horizontal line plot that uses shade or color to differentiate between states on a categorical longitudinal variable for multiple participants. With appropriate sorting, stacking the horizontal lines that represent each participant can reveal important patterns such as the shape of, or heterogeneity in, the trajectories. We illustrate the plotting techniques for large sample sizes, observed groups, the exploration of unobserved latent classes, large numbers of time points such as are found with intensive longitudinal designs or multivariate time series data, individually varying times observation, unique numbers of observations, and missing data. We used the R package longCatEDA to create the illustrations. Illustrative data include both simulated data and alcohol consumption data in adult schizophrenics from the Clinical Antipsychotic Trials of Intervention Effectiveness.