I regularly scan James Fee's great Spatially Adjusted blog for news from the ESRI side of the blogosphere. One of his favorite ideas is that ArcWeb services are equally good for web mashups as Google Maps. Besides being untrue -- SOAP is an impediment to mashups -- it's wrong-headed.
Yes, one can use the ArcWeb SOAP API to push point data to the service to be rendered onto a map and display the resulting map image in a web page, but this is not what we're talking about when we say mashup. A web map mashup, in the chicagocrime.org sense, combines data (locations, images, etc) and maps in your browser. The browser is where the mashing occurs, increasingly with the use of tools like Greasemonkey, not a GIS server.
Furthermore, a mashup begins as an unsanctioned operation or workaround for some web service that has no useful API. ArcWeb services, on the other hand, are strictly defined in order to appeal not to mashers and hackers, but to the Enterprise (managers, I mean, not the USS Enterprise). Calling the normal use of this business-suited SOAP API a "mashup" seems a bit phony, an attempt to co-opt buzz and cool.