Turbulent spin dynamics arising from the joint action of radiation damping and the distant dipolar field are shown to generate irreproducible measurements in popular high-field, gradient-based magnetic resonance (MR) experiments, undermining the prevailing assumption of essentially predictable observables in MR. Sizeable fluctuations in echo amplitudes are reported and numerically simulated for pulsed gradient spin echo and stimulated echo diffusion measurements. The underlying microscopic dynamical instability is characterized by analysis of the finite-time Lyapunov exponents. Perturbations to the modulated magnetization are shown to render magic-angle gradients ineffective in suppressing signal fluctuations. Alternative approaches are suggested for cancelling out the feedback interactions leading to spin turbulence.