I think the Nearest Neighbor Algorithm is one of the least used, and most powerful algorithms I know of. It allows me to connect data points with other data points that are similar. When something is unpredictable, or I simply don't have enough data, this allows me to compare one data point with its nearest neighbors.
So, last night I was at school, taking a graduate level Econ course. We were discussing various distance algorithms for a nearest neighbor algorithm. Our prof discussed one called the Mahalanobis distance. It uses some fancy matrix algebra. Essentially it allows it it to filter out the noise, and only match on distance algorithms that are truly significant. It takes into account the correlation that may exists within variables, and reduces those variables down to only one.
I use Nearest Neighbor when other things aren't working for me. When my data sets are weak, sparse, or otherwise not predictable. Sometimes I don't know that particular variables are correlated. This is a powerful algorithm that could be added into the Nearest Neighbor, to allow for matches that might not otherwise be found. And allow matches on only the variables that really matter.