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This paper introduces a practical index for approximate similarity queries of large multi-dimensional data sets: the spatial approximation sample hierarchy (SASH). A SASH is a multi-level structure of random samples, recursively constructed by building a SASH on a large randomly selected sample of data objects, and then connecting each remaining object to several of their approximate nearest neighbors from within the sample. Queries are processed by first locating approximate neighbors within the sample, and then using the pre-established connections to discover neighbors within the remainder of the data set. The SASH index relies on a pairwise distance measure, but otherwise makes no assumptions regarding the representation of the data. Experimental results are provided for query-by-example operations on protein sequence, image, and text data sets, including one consisting of more than 1 million vectors spanning more than 1.1 million terms 驴 far in excess of what spatial search indices can handle efficiently. For sets of this size, the SASH can return a large proportion of the true neighbors roughly 2 orders of magnitude faster than sequential search.