  We present the results of a simple but robust morphological classification of
a statis- tically complete sample of 108 of the most X-ray luminous clusters at
0.15 < z < 0.7 observed with Chandra. Our aims are to (a) identify the most
disturbed massive clusters to be used as gravitational lenses for studies of
the distant universe and as probes of particle acceleration mechanisms
resulting in non-thermal radio emission, (b) find cluster mergers featuring
subcluster trajectories that make them suitable for quantitative analyses of
cluster collisions, and (c) constrain the evolution with redshift of the
cluster merger fraction. Finally, (d) this paper represents the third public
release of clusters from the MACS sample, adding 24 clusters to the 46
published previously. To classify clusters by degree of relaxation, we use the
projected offset of the brightest cluster galaxy from the peak (or the global
centroid) of the X-ray emission as a measure of the segregation between the
intracluster gas and dark matter. Regarding (a), we identify ten complex
systems likely to have undergone multiple merger events in the recent past.
Regarding (b), we identify eleven systems likely to be post-collision, binary,
head-on mergers (BHOMs), as well as another six mergers that are possible BHOMs
but probably harder to interpret because of non-negligible impact parameters
and merger axes closer to our line of sight. Regarding (c), we find a highly
significant increase with redshift in the fraction of morphologically disturbed
clusters starting at z \sim 0.4, in spite of a detection bias in our sample
against very disturbed systems at high redshift. A larger sample of clusters
with high-quality X-ray data in particular at high redshift will be needed to
trace the evolutionary history of cluster growth and relaxation closer to the
primary epoch of cluster formation z \sim 1.
