  We establish counting formulas and bijections for deformations of the braid
arrangement. Precisely, we consider real hyperplane arrangements such that all
the hyperplanes are of the form $x\_i-x\_j=s$ for some integer $s$. Classical
examples include the braid, Catalan, Shi, semiorder and Linial arrangements, as
well as graphical arrangements. We express the number of regions of any such
arrangement as a signed count of decorated plane trees. The characteristic and
coboundary polynomials of these arrangements also have simple expressions in
terms of these trees. We then focus on certain "well-behaved" deformations of
the braid arrangement that we call transitive. This includes the Catalan, Shi,
semiorder and Linial arrangements, as well as many other arrangements appearing
in the literature. For any transitive deformation of the braid arrangement we
establish a simple bijection between regions of the arrangement and a set of
plane trees defined by local conditions. This answers a question of Gessel.
