In our work we often build applications that overlay data visualizations on top of the basemap. While the cartography of the included basemap options in ArcGIS.com is nice, none of the options work very well for overlaying data layers.
It would be nice to have a basemap option that is more muted while still retaining streets, buildings, etc. The idea being that the basemap cartography gives context to the data being layed on top instead of drawing attention away from the data.
This is an example of what I mean by a muted basemap from Cloudmade (which is based on OSM):