Let G be an acyclic directed graph. For each vertex of G, we define an involution on the independent sets of G. We call these involutions flips, and use them to define the independence poset for G--a new partial order on independent sets of G.  Our independence posets are a generalization of distributive lattices, eliminating the lattice requirement: an independence poset that is a graded lattice is always a distributive lattice. Many well-known posets turn out to be special cases of our construction.