Preferred order of writing latitude & longitude tuples in GIS services

The prefered order is by convention latitude, longitude. This was presumably standardized by the International Maritime Organization as reported here. Google also uses this order in its Maps and Earth. I remember this order by thinking of alphabetic order of latitude, longitude.

The correct order is longitude, latitude, in virtually all professional GIS applications, as it is in conventional math (ie, f(x ,y, z)). The GeoJSON standard is fairly typical and succinct:

The order of elements must follow x, y, z order
(easting, northing, altitude for coordinates in a 
projected coordinate reference system, or longitude,
latitude, altitude for coordinates in a geographic
coordinate reference system).

The same is true of the primary Open Geospatial Consortium standards (WKT and WKB, and extensions like EWKB). Likewise Google may output the order in Lat/Lon to make it more familiar to users who grew up with that custom (ie from navigation standards like IMO, rather than computational ones.) But the KML standard itself is like virtually all other GIS systems:

The KML encoding of every kml:Location and coordinate
tuple uses geodetic longitude, geodetic latitude, and
altitude (in that order).

Good rule of thumb: if you know what a tuple is and are programming, you should be using lon,lat. I would even say this applies if your end user (say a pilot or a ship captain) will prefer to view the output in lat,lon. You can switch the order in your UI if necessary, but the overwhelming majority of your data (shapefiles, geojson, etc.) will be in the normal Cartesian order.

EPSG:4326 specifically states that the coordinate order should be latitude, longitude. Many software packages still use longitude, latitude ordering. This situation has wreaked unimaginable havoc on project deadlines and programmer sanity.

The best guidance one can offer is to be fully aware of the expected axis order of each component in your software stack. PostGIS expects lng/lat. WFS 1.0 uses lng/lat, but WFS 1.3.0 defers to the standard and uses lat/lng. GeoTools defaults to lat/lng but can be overridden with a system property.

The GeoTools docs on the history and explanation of the problem are worth a read: http://docs.geotools.org/latest/userguide/library/referencing/order.html