Mirador, a collaborative effort led by Andrés Colubri from Fathom Information Design, is a tool that helps you find correlative patterns in datasets with a lot of variables and observations. It's in the early stages of development, but is available to use and test on Windows and Mac. Colubri explains the process, from its early stages to its current iteration.
Although fields like Machine Learning and Bayesian Statistics have grown enormously in the past decades and offer techniques that allows the computer to infer predictive models from data, these techniques require careful calibration and overall supervision from the expert users who run these learning and inference algorithms. A key consideration is what variables to include in the inference process, since too few variables might result in a highly-biased model, while too many of them would lead to overfitting and large variance on new data (what is called the bias-variance dilemma.)
Leaving aside model building, an exploratory overview of the correlations in a dataset is also important in situations where one needs to quickly survey association patterns in order to understand ongoing processes, for example, the spread of an infectious disease or the relationship between individual behaviors and health indicators.