I spent a couple of hours researching the Google Maps and Google Eart projection question. Found a lot of information, but had to piece together the full story. I'd appreciate any corrections to my investigations.
GOOGLE MAPS
I am currently using a spatial reference with a EPSG code of 102113 for ArcGIS Server map services that are to support mashups with Google Maps.. This is the original Web Mercator code. This was later changed to 102100 for the Web Mercator Auxiliary Sphere, which was more of a sphere than 102113. Last year 102113 was changed to 3857 and adopted as the official EPSG code. 102113 and 102100 were temporary codes as the official governing body was playing hardball with Google and others -- saying that their projection was not a real projection and pretty poor science and math. Apparently they learned how to play nice in the past 18 months.
EPSG 3857 is supposed to be the best for mashups. EPSG 102113, 102100 and 3857 are supposed to be absolutely identical projections, but the latter is official and the formers are not.
In ArcGIS Server 9.3 map services ESRI published the EPSG code of either 102113 or 102100 depending on which map projection was used. In the release of 10.0 ESRI published the EPSG code of 102113 or 102100 as the official code of 3857. In the release of 9.3.1 and 10.0 SP1 ESRI reversed itself and went back to publishing the 3857 EPSG code as 102113 (the original temporary code). Google Maps recognizes this code in a mashup.
GOOGLE EARTH
Google Earth uses a WGS84 geographic projection with an ESPG code of 4326. This projection is non-spherical (and thus unlike the Google Maps projection). Esri provides a transformation to move between the two.
WMS SERVICES
Not sure about this one, but from what I can gather if you are creating an OGC WMS service then you need to use the WGS84 World Mercator projection (EPSG code of 3395). This is similar to a pure WGS84 projection, but is a Projected rather than Geographic projection.