The design and evaluation of computer systems rely heavily upon simulation. Simulation is also a major bottleneck in the iterative design process. Applications that may be executed natively on physical systems in a matter of minutes may take weeks or months to simulate. As designs incorporate increasingly higher numbers of processor cores, it is expected the times required to simulate future systems will become an even greater issue. Simulation exhibits a tradeoff between speed and accuracy. By basing experimental procedures upon known statistical methods, the simulation of systems may be dramatically accelerated while retaining reliable methods to estimate error. This thesis focuses on the acceleration of simulation through statistical processes. The first two techniques discussed in this thesis focus on accelerating single-threaded simulation via cluster sampling. Cluster sampling extracts multiple groups of contiguous population elements to form a sample. This thesis introduces techniques to reduce sampling and non-sampling bias components, which must be reduced for sample measurements to be reliable. Non-sampling bias is reduced through the Reverse State Reconstruction algorithm, which removes ineffectual instructions from the skipped instruction stream between simulated clusters. Sampling bias is reduced via the Single Pass Sampling Regimen Design Process, which guides the user towards selected representative sampling regimens. Unfortunately, the extension of cluster sampling to include multi-threaded architectures is non-trivial and raises many interesting challenges. Overcoming these challenges will be discussed. This thesis also introduces thread skew, a useful metric that quantitatively measures the non-sampling bias associated with divergent thread progressions at the beginning of a sampling unit. Finally, the Barrier Interval Simulation method is discussed as a technique to dramatically decrease the simulation times of certain classes of multi-threaded programs. It segments a program into discrete intervals, separated by barriers, which are leveraged to avoid many of the challenges that prevent multi-threaded sampling.