See: http://www.rproject.org/. R is a system for statistical computation and graphics. It consists of a language plus a runtime environment with graphics, a debugger, access to certain system functions, and the ability to run programs stored in script files. Selected spatial analysis packages are listed in the Table below. Descriptions are those provided by the package authors. Many of the Spatial functions are described at: http://cran.rproject.org/web/views/Spatial.html
An RSpatial page with news and comments is provided by Arizona State University:
http://geodacenter.asu.edu/rspatialprojects/
Package (links) 
Description 
Features 

ads 
Spatial point patterns analysis 
Perform first and secondorder multiscale analyses derived from Ripley's Kfunction, for univariate, multivariate and marked mapped data in rectangular, circular or irregular shaped sampling windows, with test of statistical significance based on Monte Carlo simulations. 
aspace 
A collection of functions for estimating centrographic statistics and computational geometries from spatial point patterns 
A collection of functions for computing centrographic statistics (e.g., standard distance, standard deviation ellipse), and minimum convex polygons (MCP) for observations taken at point locations. A tool is also provided for converting geometric objects associated with the centrographic statistics, and MCPs into ESRI Shapefiles 
DCluster 
Functions for the detection of spatial clusters of diseases 
A set of functions for the detection of spatial clusters of disease using count data. Bootstrap is used to estimate sampling distributions of statistics 
fields 
Tools for spatial data 
Fields is for curve, surface and function fitting with an emphasis on splines, spatial data and spatial statistics. The major methods include cubic, robust, and thin plate splines, multivariate Kriging and Kriging for large data sets. One main feature is any covariance function implemented in R can be used for spatial prediction. There are also useful functions for plotting and working with spatial data as images 
GeoXp 
http://cran.rproject.org/web/packages/GeoXp/index.html Interactive exploratory spatial data analysis (manual is in French) 
GeoXp is a tool for researchers in spatial statistics, spatial econometrics, geography, ecology etc allowing to link dynamically statistical plots with elementary maps. This coupling consists in the fact that the selection of a zone on the map results in the automatic highlighting of the corresponding points on the statistical graph or reversely the selection of a portion of the graph results in the automatic highlighting of the corresponding points on the map. GeoXp includes tools from different areas of spatial statistics including geostatistics as well as spatial econometrics and point processes. Besides elementary plots like box plots, histograms or simple scatterplots, GeoXp also couples with maps Moran scatterplots, variogram cloud, Lorentz Curves,...In order to make the most of the multidimensionality of the data, GeoXp includes some dimension reduction techniques such as PCA 
geoRglm 
Package for generalized linear spatial models 
Functions for inference in generalized linear spatial models. The posterior and predictive inference is based on Monte Carlo Markov chain methods. Package geoRglm is an extension to the package geoR, which must be installed first. 
grasp/grasper 
Generalized Regression Analysis and Spatial Prediction for R 
GRASP is a general method for making spatial predictions of response variables (RV) using point surveys of the RV and spatial coverages of Predictor variables (PV) 
maptools 
Tools for reading and handling spatial objects 
Set of tools for manipulating and reading geographic data, in particular ESRI shapefiles. Includes facilities for Google Earth grid and KML creation, ASCII grid reading, output to Mondrian, WinBUGS etc. 
spatial 
Functions for Kriging and Point Pattern Analysis 

sp 
A package that provides classes and methods for spatial data. Note that sp has its own Sourceforge page. see: 
The classes document where the spatial location information resides, for 2D or 3D data. Utility functions are provided, e.g. for plotting data as maps, spatial selection, as well as methods for retrieving coordinates, for subsetting, print, summary, etc. 
spBayes 
Univariate and Multivariate Spatial Modeling 
spBayes fits Gaussian univariate and multivariate models with Monte Carlo Markov chain (MCMC) 
spatclus 
Arbitrarily Shaped Multiple Spatial Cluster Detection for Case Event Data 
Multiple cluster location and detection for 2D and 3D spatial point patterns (case event data). The methodology of this package is based on an original method that allows the detection of multiple clusters of any shape. A selection order and the distance from its nearest neighbor once preselected points have been taken into account are attributed at each point. This distance is weighted by the expected distance under the uniform distribution hypothesis. Potential clusters are located by modeling the multiple structural change of the distances on the selection order. Their presence is tested using the double maximum test and a Monte Carlo procedure 
spatgraphs 
Graphs for spatial point patterns 
Graphs, graph visualization and graph component calculations, meant to be used as a tool in spatial point pattern analysis 
spatstat 
http://cran.rproject.org/web/packages/spatstat/index.html Spatial Point Pattern analysis, modelfitting, simulation, tests. See further 
A package for analyzing spatial data, mainly Spatial Point Patterns, including multitype/marked points and spatial covariates, in any twodimensional spatial region. Contains functions for plotting spatial data, exploratory data analysis, modelfitting, simulation, spatial sampling, model diagnostics, and formal inference. Data types include point patterns, line segment patterns, spatial windows, and pixel images. Point process models can be fitted to point pattern data. Cluster type models are fitted by the method of minimum contrast. Very general Gibbs point process models can be fitted to point pattern data using a function ppm similar to lm or glm. Models may include dependence on covariates, interpoint interaction and dependence on marks. Fitted models can be simulated automatically. Also provides facilities for formal inference (such as chisquared tests) and model diagnostics (including simulation envelopes, residuals, residual plots and QQ plots) 
spdep 
Spatial dependence: weighting schemes, statistics and models. See documentation for details: 
A collection of functions to create spatial weights matrix objects from polygon contiguities, from point patterns by distance and tessellations, for summarizing these objects, and for permitting their use in spatial data analysis, including regional aggregation by minimum spanning tree; a collection of tests for spatial autocorrelation, including global Moran's I, APLE, Geary's C, Hubert/Mantel general cross product statistic, Empirical Bayes estimates and Assunção/Reis Index, Getis/Ord G and multicolored join count statistics, local Moran's I and Getis/Ord G, saddlepoint approximations and exact tests for global and local Moran's I; and functions for estimating spatial simultaneous autoregressive (SAR) lag and error models, weighted and unweighted SAR and CAR spatial regression models, semiparametric and Moran eigenvector spatial filtering, GM SAR error models, and generalized spatial two stage least squares models 
spgwr 
Geographically weighted regression 
The function implements generalized geographically weighted regression approach to exploring spatial nonstationarity for given global bandwidth and chosen weighting scheme. 
splancs 
Spatial and SpaceTime Point Pattern Analysis in R and S 
Point pattern analysis, including kernel density, Ripley K, Ghat and Fhat functions 
trip 
Trip pattern analysis 
Analysis of spatial trip data, notably animal tracking information 