Complex systems such as those in evolution, growth and depinning models do not evolve slowly and gradually, but exhibit avalanche dynamics or punctuated equilibria. Self-Organized Criticality (SOC) and Highly Optimized Tolerance (HOT) are two theoretical models that explain such avalanche dynamics. We have studied avalanche dynamics in two vastly different grid computing systems: Optimal Grid and Vishva. Failures in optimal grid cause an avalanche effect with respect to the overall computation. Vishva does not exhibit failure avalanches. Interestingly, Vishva exhibits load avalanche effects at critical load density, wherein a small load disturbance in one node can cause load disturbances in several other nodes. The avalanche dynamics of grid computing systems implies that grids can be viewed as SOC systems or as HOT systems. An SOC perspective suggests that grids may be sub-optimal in performance, but may be robust to unanticipated uncertainties. A HOT perspective suggests that grids can be made optimal in performance, but would then be sensitive to unanticipated perturbations. An ideal approach for grid systems research is to explore a combination of SOC and HOT as a basis for design, resulting in robust yet optimal systems.