Changes in ionospheric plasma densities can affect society more than ever because of our increasing reliance on communication, surveillance, navigation, and timing technology. Models struggle to predict changes in ionospheric densities at nearly all temporal and spatial scales, especially during geomagnetic storms. Here we combine a 50 year (1965–2015) geomagnetic disturbance storm time (Dst) index with plasma density measurements from a worldwide network of ~132 vertical incidence ionosondes to develop a picture of global scale changes in peak plasma density due to geomagnetic storms. Vertical incidence ionosondes provide measurements of the critical frequency of the ionospheric F2 layer (foF2), a direct measure of the peak electron density (NmF2) of the ionosphere. By dissecting the NmF2 perturbations with respect to the local time at storm onset, season, and storm intensity, it is found that (i) the storm‐associated depletions (negative storm effects) and enhancements (positive storm effects) are driven by different but related physical mechanisms, and (ii) the depletion mechanism tends to dominate over the enhancement mechanism. The negative storm effects, which are detrimental to HF radio links, are found to start immediately after geomagnetic storm onset in the nightside high‐latitude ionosphere. The depletions in the dayside high‐latitude ionosphere are delayed by a few hours. The equatorward expansion of negative storm effects is found to be regulated by storm intensity (farthest equatorward and deepest during intense storms), season (largest in summer), and time of day (generally deeper on the nightside). In contrast, positive storm effects typically occur on the dayside midlatitude and low‐latitude ionospheric regions when the storms are in the main phase, regardless of the season. Closer to the magnetic equator, moderate density enhancements last up to 40 h during the recovery phase of equinox storms, regardless of the local time. Strikingly, high‐latitude plasma densities are moderately enhanced for up to 60 h prior to the actual onset of storms during the equinoxes and summer; a potential precursor of a geomagnetic storm.