Pulsars are famed for their rotational clock-like stability and their highly-repeatable pulse shapes. However, it has long been known that there are unexplained deviations (often termed timing noise) from the rate at which we predict these clocks should run. We show that timing behaviour often results from typically two different spin-down rates. Pulsars switch abruptly between these states, often quasi-periodically, leading to the observed spin-down patterns. We show that for six pulsars the timing noise is correlated with changes in the pulse shape. Many pulsar phenomena including mode-changing, nulling, intermittency, pulse shape variability and timing noise are therefore linked and caused by changes in the pulsars magnetosphere. We consider the possibility that high-precision monitoring of pulse profiles could lead to the formation of highly-stable pulsar clocks.