A number of open source spatial analysis tools are available. Often, they are created by leading researchers and practitioners in the field.
For ESRI's ArcGIS, different license levels leave out key features. For example, you will need an ArcGIS Advanced (formerly ArcInfo) license to create Thiessen/Voronoi polygons. An ArcGIS basic license with Spatial Analyst extension will allow you to perform geographically weighted regression (GWR) but you will need an ArcGIS advanced license to create spatial weights based on contiguity (i.e. queen, rook). ESRI does list what is included in the different versions of its software in a functionality matrix you can find here: www.esri.com/library/brochures/pdfs/arcgis10-desktop-functionality-matrix.pdf.
Fortunately, alternatives are available -- including open source tools that are accessible and will link into ArcGIS. I touch on three here, but numerous other tools, packages, and plugins exist mainly based on Python.
Geospatial Modelling Environment, formerly known as "Hawthe's Tools." A full list of its commands can be found at: http://www.spatialecology.com/gme/gmecommands.htm
Arizona State University provides a number of spatial tool including GeoDA and PySAL.
SaTScan dives into the temporal and spatiotemporal dimensions.
GWR4 is available for performing GWR for poisson data and other non-linear data distributions. It can be found at: http://gwr.nuim.ie/node/6
In future posts, I will show several examples and, time allowing, also compare the results with ArcGIS.