The following links are from my presentation at the MAPSS seminar, which provided an overview of the resources to get started with GIS research in the Social Sciences.  Note that some pointers have relevance or are accessible for Stanford affiliates only.

Software:

ArcGIS -  http://esri.com

ArcGIS is an integrated collection of commercial GIS software products that provides a standards-based platform for spatial analysis, data management, and mapping. Windows only.

CrimeStat http://www.icpsr.umich.edu/CRIMESTAT

CrimeStat is a spatial statistics program, originally developed for the analysis of crime incident locations. The program inputs incident locations in 'dbf', 'shp', ASCII or ODBC-compliant formats using either spherical or projected coordinates. It calculates various spatial statistics, like for example, nearest neighbor, spatial clustering, or point pattern, and writes graphical objects to ArcGIS and other GIS programs. Windows only.

GRASS-GIS http://grass.itc.it

GRASS is a Geographic Information System (GIS) used for geospatial data management and analysis, image processing, graphics/maps production, spatial modeling, and visualization. Free, open source and runs on all platforms.

ENVI http://www.ittvis.com/envi

ENVI is a commercial software solution for processing and analyzing geospatial imagery. It offers the latest spectral image processing and image analysis technology.

GeoDa http://geodacenter.asu.edu

GeoDa is a ollection of software tools designed to implement techniques for exploratory spatial data analysis (ESDA) on lattice data. It is intended to provide a user friendly and graphical interface to methods of descriptive spatial data analysis, such as autocorrelation statistics and indicators of spatial outliers. Free and currently Windows only.

Mondrian http://stats.math.uni-augsburg.de/Mondrian/

Mondrian is a general purpose statistical data-visualization system. It features outstanding visualization techniques for data of almost any kind, and has its particular strength compared to other tools when working with Categorical Data, Geographical Data and large Datasets.  All plots in Mondrian are fully linked, and offer various interactions and queries. Free and runs on all platforms.

Books:

Chang, Kang-tsung 2009: Introduction to Geographic Information Systems. McGraw-Hill; 5th edition

Maribeth H. Price 2009: Mastering ArcGIS. McGraw-Hill; 4th edition

Neteler, Markus & Helena Mitasova 2008: Open Source GIS: A GRASS GIS Approach. Springer

Bivand, Roger S., Pebesma, Edzer J., Gómez-Rubio, Virgilio 2008: Applied Spatial Data Analysis with R. Springer

Goodchild, Michael F. , Donald G. Janelle 2004: Spatially Integrated Social Science. Oxford University 2004

Parker, Robert Nash, Parker, Emily K Asencio 2008: GIS and Spatial Analysis for the Social Sciences - Coding, Mapping, and Modeling. Routledge.

Lists:

GRASS user list grass-user

The principal GRASS mailing list, for discussion about problems and solutions using GRASS.

R Special Interest Group on using Geographical data and Mapping R-sig-Geo

A mailing list for discussing the development and use of R functions and packages for handling and analysis of spatial, and particularly geographical, data. The list also covers mapping and cartographic issues, and interfaces between R and geographical information systems.

The following links are provided by Julie Sweetkind, Head of the Stanford Branner Earth Sciences Library:

Finding GIS Data at Branner Library

Searching in Socrates
Place + “geographic information systems data”

GIS data on the AFS space
http://library.stanford.edu/depts/gis/afsdata.html

GIS Datasets at Branner
http://www-sul.stanford.edu/depts/gis/datasets.html

Finding GIS Data outside the Library

Seamless USGS topographic maps
http://seamless.usgs.gov/index.php

Websites for finding GIS data
http://www-sul.stanford.edu/depts/gis/web.html

Social Science Data and Software (numeric and statistical data)
http://ssds.stanford.edu

Census data
American Factfinder (Census Bureau) http://factfinder.census.gov
NHGIS (National Historical GIS): http://nhgis.org
IPUMS International (Integrated Public Use Microdata Series): http://international.impums.org/international/

Other resources
SEDAC (Socioeconomic Data and Applications Center): http://sedac.ciesin.columbia.edu/
CASIL (California Spatial Information Library): http://gis.ca.gov

School of Earth Sciences loans out GPS units (to Stanford affiliates).