  Depending on the stellar type, more than $\sim 50$\% and $\sim 15\%$ of stars
in the field have at least one and two stellar companions, respectively.
Hierarchical systems can be assembled dynamically in dense star clusters, as a
result of few-body encounters among stars and/or compact remnants in the
cluster core. In this paper, we present the demographics of stellar and
compact-object triples formed via binary--binary encounters in the \texttt{CMC
Cluster Catalog}, a suite of cluster simulations with present-day properties
representative of the globular clusters (GCs) observed in the Milky Way. We
show how the initial properties of the host cluster set the typical orbital
parameters and formation times of the formed triples. We find that a cluster
typically assembles hundreds of triples with at least one black hole (BH) in
the inner binary, while only clusters with sufficiently small virial radii are
efficient in producing triples with no BHs, as a result of the BH-burning
process. We show that a typical GC is expected to host tens of triples with at
least one luminous component at present day. We discuss how the Lidov-Kozai
mechanism can drive the inner binary of the formed triples to high
eccentricities, whenever it takes place before the triple is dynamically
reprocessed by encountering another cluster member. Some of these systems can
reach sufficiently large eccentricities to form a variety of transients and
sources, such as blue stragglers, X-ray binaries, Type Ia Supernovae,
Thorne-Zytkow objects, and LIGO/Virgo sources.
