  Cosmological galaxy formation simulations can now produce rich and diverse
ensembles of galaxy histories. These simulated galaxy histories, taken all
together, provide an answer to the question "how do galaxies form?" for the
models used to construct them. We characterize such galaxy history ensembles
both to understand their properties and to identify points of comparison for
histories within a given galaxy formation model or between different galaxy
formation models and simulations. We focus primarily on stellar mass histories
of galaxies with the same final stellar mass, for six final stellar mass values
and for three different simulated galaxy formation models (a semi-analytic
model built upon the dark matter Millennium simulation and two models from the
hydrodynamical OverWhelmingly Large Simulations project). Using principal
component analysis (PCA) to classify scatter around the average stellar mass
history, we find that one fluctuation dominates for all sets of histories we
consider, although its shape and contribution can vary between samples. We
correlate the PCA characterization with several $z=0$ galaxy properties (to
connect with survey observables) and also compare it to some other galaxy
history properties. We then explore separating galaxy stellar mass histories
into classes, using the largest PCA contribution, k-means clustering, and
simple Gaussian mixture models. For three component models, these different
methods often gave similar results. These history classification methods
provide a succinct and often quick way to characterize changes in the full
ensemble of histories of a simulated population as physical assumptions are
varied, to compare histories of different simulated populations to each other,
and to assess the relation of simulated histories to fixed time observations.
