After double tapping G with an edge-ring selected, you enter edge-slide mode now press E to access a model operator that attempts to align the edge-ring with either of the neighboring edge-rings. You can choose which parallel ring to align with by pressing the F key.
Note that that the header also shows the keys:
The same thing works for Loop Cut and Slide Ctrl+r, the only problem this function is that it works best for meshes that are uniform along all three axis. If the object is really long along one axis; the edge-align tool will behave as if the Object has non-uniform scale even if it does not.