We analyze the structure of reduced expressions in the Coxeter groups
A
n
A_{n}
,
B
n
B_{n}
and
D
n
D_{n}
. Several special classes of elements are singled out for their connections with symmetric functions or the theory of
P
P
-partitions. Membership in these special classes is characterized in a variety of ways, including forbidden patterns, forbidden subwords, and by the form of canonically chosen reduced words.