(The following contains mathematical formula and symbols that may become distorted in ASCII text.) New methods for parallelizing Ising model simulations are presented. A parallel single-spin Metropolis algorithm has been implemented with a speedup of 27 on 50 processors of the KSR-1 parallel computer. Our parallel Swendsen-Wang algorithm obtains a speedup of 3.2 on 9 processors of the same computer. Both of these simulations were carried out on 200x200 lattices. The parallel Local Cluster algorithm has been implemented with an almost linear speedup. We also discuss ongoing research using the parallel Local Cluster algorithm.