Implementing traditional forms of multiprocess synchronization requires a hardware arbiter. Here, we consider what kind of synchronization is achievable without arbitration. Several kinds of simple arbiter-free registers are defined and shown to have equal power, and the class of synchronization problems solvable with such registers is characterized. More powerful forms of arbiter-free communication primitives are described. However, the problem of characterizing the most general form of arbiter-free synchronization remains unsolved.