ArcGIS Engine

The ESRI product "ArcGIS Engine" is a set of libraries that can be used by GIS application developers to create either add-ons for other ESRI products or free-standing applications.

To deploy the free-standing application to a machine that does not have ArcGIS Desktop installed on it you include the ArcGIS Engine Runtime in the deployment. There is a $500/seat license for the Runtime.

There are also extensions for the runtime corresponding to the ArcGIS Desktop extensions. These include Spatial Analyst, 3D Analyst, Network Analyst, and Geostatistical Analyst. I am not sure of the cost of the licensing for the extensions.