Neuronal dendritic spines are a key component of brain circuitry, implicated in many mechanisms for plasticity and long-term stability of synaptic communication. They can undergo rapid actin-based activity-dependent shape fluctuations, an intriguing biophysical property that is believed to alter synaptic transmission. Yet, because of their small size (approximately 1 microm or less) and metastable behavior, spines are inaccessible to most physical measurement techniques. Here we employ atomic force microscopy elasticity mapping and novel dynamic indentation methods to probe the biomechanics of dendritic spines in living neurons. We find that spines exhibit 1), a wide range of rigidities, correlated with morphological characteristics, axonal association, and glutamatergic stimulation, 2), a uniquely large viscosity, four to five times that of other cell types, consistent with a high density of solubilized proteins, and 3), weak power-law rheology, described by the soft-glassy model for cellular mechanics. Our findings provide a new perspective on spine functionality and identify key mechanical properties that govern the ability of spines to rapidly remodel and regulate internal protein trafficking but also maintain structural stability.