Conscious experience is dynamic, and its fluidity is particularly marked when attention is not occupied by events in the external world and our minds are free to wander. Our study used measures of neural function, and advanced analyses techniques to examine how unconstrained neural state transitions relate to patterns of ongoing experience. Neural activity was recorded during wakeful rest using functional magnetic resonance imaging and Hidden Markov modelling identified recurrent patterns of brain activity constituting functional dynamic brain states. Individuals making more frequent transitions between states subsequently described experiences highlighting problem solving and lacking unpleasant intrusive features. Frequent switching between states also predicted better health and well-being as assessed by questionnaire. These data provide evidence that the fluidity with which individuals shift through dynamic neural states has an impact on the nature of ongoing thought, and suggest that greater flexibility at rest is an important indicator of a healthy mind.