This has been an annoying problem for a while, and hopefully will no longer be an issue.
3857 looks to be the current and correct code (I hope, that's what all my tile caches are in!).
Update 9/7/11 - as noted by Vadim below in comments, Esri did in fact revert back to 102100 from 3857 at Service Pack 1. Oddly, ArcGIS Server with SP1 applied returns a WKID of 102100 for a web mercator map service, but in the Services Directory, a web mercator map service has a spatial reference of '102100 (3857)'. EPSG has no entry for 102100. Not sure why Esri has chosen this route, but Esri's 102100 and 3857 are treated as equivalent by their products.
EPSG - (no direct link)
Request: Revisit spherical mercator used for some web mapping applications
Actions Taken: Deprecated ellipsoid 7059, datum 6055, method 9841, projection 19847, CRSs 4055 and 3785, tfm 15973. Added methods 1024 and 1026, proj 3856 and projCRS 3857.
Entity Types Affected: Ellipsoid; Datum; Coordinate Operation Method; Coordinate Operation; Coordinate Reference System
Codes Affected: 7059; 6055; 9841; 15973 19847; 4055 3785
Report Date (UTC): 2008-12-11
Closed Date (UTC): 2009-02-10
Today, there is an officially registered EPSG code 3857 whose projection is identical to EPSG:900913. (http://www.epsg-registry.org/export.htm?gml=urn:ogc:def:crs:EPSG::3857). So, if you need to combine overlay layers that are using either an alias or the official EPSG code with an OpenLayers SphericalMercator layer, you have to make sure that OpenLayers requests EPSG:3857 or other alias in stead of EPSG:900913.
@jamie - For a long time EPSG refused to assign a code to this coordinate system; therefore ESRI created the WKID codes 102113 and 102100.
When EPSG did assign a code, they used 3785, but later changed it to 3857. ArcGIS 10 will follow ESRI practice of using an EPSG code when one exists, and will advertise the coordinate system of the service as 3857. ArcGIS 10 and all Web APIs are being designed to recognize EPSG 3857, ESRI WKID 102113, and ESRI WKID 102100 as equivalent.