R

R is a programming language for statistics. R includes a huge statistics package. Command line only, but very powerful. There are also a lot of contributions outside the "core" project.

R has grown to the major S implementation with an unimaginable count of example code, libraries and extensions - the first choice for scientific computing, not only in statistics, also for simulation, modelling and mathematical graphics.

When it comes to statistics, machine learning, data science, etc. R always has the very latest algorithms. It's a programming environment and although there are a couple of menu systems such as R Commander and Deducer, they only cover a tiny proportion of R's overall capability. RStudio is the most popular programming front-end to R and it is open source too. If you want to combine point-and-click work with R programming, you might try another open source package, KNIME. It integrates well with R.