Data mining clustering methods are usually used for exploratory purposes and to gain insights into data. The most commonly used methods include k-Means, agglomerative hierarchical clustering and increasingly self organizing maps. The tools listed below support a wide variety of methods, some of which are particular to a given toolset.
Toolkits
Databionic ESOM Tools is a suite of programs to perform data mining tasks like clustering, visualization, and classification with Emergent Self-Organizing Maps (ESOM).
KEEL is an open source (GPLv3) Java software tool to assess evolutionary algorithms for Data Mining problems including regression, classification, clustering, pattern mining and so on. It supports k-Means clustering.
mlpy is a Python module for Machine Learning built on top of NumPy/SciPy and the GNU Scientific Libraries. It includes k-Means and Hierarchical Clustering.
PermutMatrix provides data visualizations with clustering and seriation analysis. It supports hierarchical clustering.
scikit-learn provides many easy to use tools for data mining and analysis. It is built on python and specifically NumPy, SciPy and matplotlib, and supports many clustering methods including k-Means, affinity propagation, spectral clustering, Ward hierarchical clustering, agglomerative clustering (hierarchical), Gaussian mixtures and Birch clustering.
General Purpose Data Mining Platforms
KNIME is a general purpose data mining platform with over 1000 different operators. Its support for clustering includes k-Means, k-Mediods, Hierarchcial Clustering, Fuzzy c-Means and SOTA (self organizing tree algorithm).
Orange is a (relatively) easy to use data mining platform with support for hundreds of operators. The clustering methods it supports include k-Means, SOM (self organizing maps), Hierarchical Clustering, and MDS (multi-dimensional scaling).
RapidMiner Community Edition is perhaps the most widely used visual data mining platform and supports Hierarchical Clustering, Support Vector Clustering, Top Down Clustering, k-Means and k-Mediods.
Tanagra supports a variety of methods including k-Means, SOM, LVQ (Learning Vector Quantizers) and Hierarchical Clustering
Weka is a platform whose algorithms are used in many other toolkits (RapidMiner for example). Clustering methods include DBSCAN, COBWEB (creates a classification tree), k-Means and the EM (expectation maximization) algorithm.