When to enable 'On the fly' CRS transformation in QGIS? When to turn it off?

The rule is simple: the on-the-fly reprojection is useful only when you are dealing with layers which have a different CRS and only when your purpose is visualizing multiple layers at once.

Instead, great care is needed when you want to perform spatial operations or when you are visualizing their results because, in general, the rendering of the layers doesn't match to the real results.

In conclusion, it is only thought for the displaying of layers which have different source CRS. You may always have it enabled, but I think that the unique rule-of-thumb is remembering it is activated.

I generally prefer to work with layers which have the same CRS and, if this doesn't happen, I reproject the layers of interest to the same CRS: following this philosophy, the on-the-fly reprojection is generally disabled. I enable it only when I need to quickly visualising some layers or when dealing with WMS services because they are generally provided using Geographic Coordinate Systems.

There is no correct or not correct. Crucial about On the fly is, that you have to know well your data.

Simplified: with enabling On the fly you're telling QGIS, that you want all data "display" in given CRS.

Deactivating On the fly you will see all data displayed in your QGIS project CRS based on data geometries - when data CRS is different than Project CRS, these data will be displayed in wrong place.