Data sets of well known case studies have been made available here after.
Spatial Interpolation Comparison 97
The data sets used for SIC97 (Spatial Interpolation Comparison 97) can be found here as well as with a description of these files. The whole report on this international statistical exercise can be found in the "Events" section of AI-GEOSTATS.
Spatial Interpolation Comparison 2004
The data sets used for SIC2004 (Spatial Interpolation Comparison 2004) can be found here . The data and the whole international statistical exercise are described in the "Events" section of AI-GEOSTATS.
Data analysed in books about geostatistics
The Jura data sets (measurements of several elements taken from soil samples) from Pierre Goovaerts' book are available at the end of his book's web page: Goovaerts, P. 1997. Geostatistics for Natural Resources Evaluation. Oxford Univ. Press, New-York. See http://goovaerts.pierre.googlepages.com/
The Walker Lake data set from Isaak & Srivastava's book (Applied Geostatistics) is available here. You can download the exhaustive dataset (around 1 MB, zipped) and the subset used as a test set.
Mining data and also a few other types presented in Isobel Clark's book (Practical Geostatistics 2000) can be accessed from http://www.kriging.com/datasets/ and used with a teaching software that is freely distributed.