In this paper, we present triggered instructions, a novel control paradigm for arrays of processing elements (PEs) aimed at exploiting spatial parallelism. Triggered instructions completely eliminate the program counter and allow programs to transition concisely between states without explicit branch instructions. They also allow efficient reactivity to inter-PE communication traffic. The approach provides a unified mechanism to avoid over-serialized execution, essentially achieving the effect of techniques such as dynamic instruction reordering and multithreading, which each require distinct hardware mechanisms in a traditional sequential architecture. Our analysis shows that a triggered-instruction based spatial accelerator can achieve 8× greater area-normalized performance than a traditional general-purpose processor. Further analysis shows that triggered control reduces the number of static and dynamic instructions in the critical paths by 62% and 64% respectively over a program-counter style spatial baseline, resulting in a speedup of 2.0×.