In general, there is no way to clip the data. However, depending on what application you are using to create your maps, it is possible to restrict the display to a particular area.
In the ArcGIS.com map viewer, there is no way currently to restrict the visible extent of the data. In ArcGIS Desktop (ArcMap) it is possible to restrict the extent of the data frame to a specified extent. Thus, a user wouldn't be able to zoom out past your area of interest. There is a property on the data frame that sets this.
Hope this helps,
Mike