To express whuber's answer in terms of tool use, here's a simple implementation of the North-South, East-West use case when using point data in Arcgis:

• Add X and Y (or Lat and Long) columns to the attribute table, Calculate Geometry
• export to Excel or whatever, sort by the column of interest (X for East-West, Y for North-South), and then bring back in with Add X/Y data.

courtesy of Esri Technical Article HowTo: Sort features North/South or East/West for Export

Changing order of features in shapefile has solutions to do the table sorting part for both Arcgis and Qgis without need to export to an external program (though you still need to duplicate the table/feature class), and Sorting shapefile records on attribute to update new rank field using ArcPy? has an arcpy method.

To express whuber's answer in terms of tool use, here's a simple implementation of the North-South, East-West use case when using point data in Arcgis:

• Add X and Y (or Lat and Long) columns to the attribute table, Calculate Geometry
• export to Excel or whatever, sort by the column of interest (X for East-West, Y for North-South), and then bring back in with Add X/Y data.

courtesy of Esri Technical Article HowTo: Sort features North/South or East/West for Export

Changing order of features in shapefile has solutions to do the table sorting part for both Arcgis and Qgis without need to export to an external program (though you still need to duplicate the table/feature class), and Sorting shapefile records on attribute to update new rank field using ArcPy? has an arcpy method.