Structure is only the first step in understanding the interactions and functions of proteins. In this paper, we explore the flexibility of proteins across a broad database of over 250 solvated protein molecular dynamics simulations in water for an aggregate simulation time of approximately 6 micros. These simulations are from our Dynameomics project, and these proteins represent approximately 75% of all known protein structures. We employ principal component analysis of the atomic coordinates over time to determine the primary axis and magnitude of the flexibility of each atom in a simulation. This technique gives us both a database of flexibility for many protein fold families and a compact visual representation of a particular protein's native-state conformational space, neither of which are available using experimental methods alone. These tools allow us to better understand the nature of protein motion and to describe its relationship to other structural and dynamical characteristics. In addition to reporting general properties of protein flexibility and detailing many dynamic motifs, we characterize the relationship between protein native-state flexibility and early events in thermal unfolding and show that flexibility predicts how a protein will begin to unfold. We provide evidence that fold families have conserved flexibility patterns, and family members who deviate from the conserved patterns have very low sequence identity. Finally, we examine novel aspects of highly inflexible loops that are as important to structural integrity as conventional secondary structure. These loops, which are difficult if not impossible to locate without dynamic data, may constitute new structural motifs.