Structure and dynamics of living matter rely on design principles fundamentally different from concepts of traditional material science. Specialized intracellular filaments in the cytoskeleton permit living systems to divide, migrate, and grow with a high degree of variability and durability. Among the three filament systems, microfilaments, microtubules, and intermediate filaments (IFs), the physical properties of IFs and their role in cellular mechanics are the least well understood. We use optical trapping of individual vimentin filaments to investigate energy dissipation, strain history dependence, and creep behavior of stretched filaments. By stochastic and numerical modeling, we link our experimental observations to the peculiar molecular architecture of IFs. We find that individual vimentin filaments display tensile memory and are able to dissipate more than 70% of the input energy. We attribute these phenomena to distinct nonequilibrium folding and unfolding of α helices in the vimentin monomers constituting the filaments.