  We say that an unordered rooted labeled forest avoids the pattern
$\pi\in\mathcal{S}_n$ if the sequence obtained from the labels along the path
from the root to any vertex does not contain a subsequence that is in the same
relative order as $\pi$. We enumerate several classes of forests that avoid
certain sets of permutations, including the set of unimodal forests, via
bijections with set partitions with certain properties. We also define and
investigate an analog of Wilf-equivalence for forests.
