Here is a summary of several clustering algorithms that can help to answer the question
"which clustering technique i should use?"
There is no objectively "correct" clustering algorithm Ref
Clustering algorithms can be categorized based on their "cluster model". An algorithm designed for a particular kind of model will generally fail on a different kind of model. For eg, k-means cannot find non-convex clusters, it can find only circular shaped clusters.
Therefore, understanding these "cluster models" becomes the key to understanding how to choose among the various clustering algorithms / methods. Typical cluster models include:
 Connectivity models: Builds models based on distance connectivity. Eg hierarchical clustering. Used when we need different partitioning based on tree cut height. R function: hclust in stats package.
 Centroid models: Builds models by representing each cluster by a single mean vector. Used when we need crisp partitioning (as opposed to fuzzy clustering described later). R function: kmeans in stats package.
 Distribution models: Builds models based on statistical distributions such as multivariate normal distributions used by the expectation-maximization algorithm. Used when cluster shapes can be arbitrary unlike k-means which assumes circular clusters. R function: emcluster in the emcluster package.
 Density models: Builds models based on clusters as connected dense regions in the data space. Eg DBSCAN and OPTICS. Used when cluster shapes can be arbitrary unlike k-means which assumes circular clusters.. R function dbscan in package dbscan.
 Subspace models: Builds models based on both cluster members and relevant attributes. Eg biclustering (also known as co-clustering or two-mode-clustering). Used when simultaneous row and column clustering is needed. R function biclust in biclust package.
 Group models: Builds models based on the grouping information. Eg collaborative filtering (recommender algorithm). R function Recommender in recommenderlab package.
 Graph-based models: Builds models based on clique. Community structure detection algorithms try to find dense subgraphs in directed or undirected graphs. Eg R function cluster_walktrap in igraph package.
 Kohonen Self-Organizing Feature Map: Builds models based on neural network. R function som in the kohonen package.
 Spectral Clustering: Builds models based on non-convex cluster structure, or when a measure of the center is not a suitable description of the complete cluster. R function specc in the kernlab package.
 subspace clustering : For high-dimensional data, distance functions could be problematic. cluster models include the relevant attributes for the cluster. Eg, hddc function in the R package HDclassif.
 Sequence clustering: Group sequences that are related. rBlast package.
 Affinity propagation: Builds models based on message passing between data points. It does not require the number of clusters to be determined before running the algorithm. It is better for certain computer vision and computational biology tasks, e.g. clustering of pictures of human faces and identifying regulated transcripts, than k-means, Ref Rpackage APCluster.
 Stream clustering: Builds models based on data that arrive continuously such as telephone records, financial transactions etc. Eg R package BIRCH [https://cran.r-project.org/src/contrib/Archive/birch/]
 Document clustering (or text clustering): Builds models based on SVD. It has used in topic extraction. Eg Carrot [http://search.carrot2.org] is an open source search results clustering engine which can cluster documents into thematic categories.
 Latent class model: It relates a set of observed multivariate variables to a set of latent variables. LCA may be used in collaborative filtering. R function Recommender in recommenderlab package has collaborative filtering functionality.
 Biclustering: Used to simultaneously cluster rows and columns of two-mode data. Eg R function biclust in package biclust.
 Soft clustering (fuzzy clustering): Each object belongs to each cluster to a certain degree. Eg R Fclust function in the fclust package.