Experimental design
PsychoPy is my preferred software for designing behavioral experiments. It is open-source, Python-backed, and has an extremely user-friendly GUI. Who writes code in visual basic these days anyway? 
JASP is the alternative to SPSS that everyone has always wanted. It does Bayesian stats on top of NHST. It provides publishable figures. And it's open-source; no annual re-licensing scams. New functions are added regularly. 
RStudio If you're serious about statistics, you ought to use R. Just about everything you've ever wanted to do with your data is possible and someone has already made an "app" for it. RStudio pulls it all together in a user-friendly way, so that you can see your code, the environment, the terminal, and the figures at the same time. 
R Tutorial  Want to use R, but don't know where to start? Dani Navarro (UNSW) has created this wonderful online tutorial aimed at psychology students and others without much programming experience. It walks you through the necessary background (programming and statistics) and provides examples for how to do some of the most commonly used stats in R.  
AFNI is a must use software for the analysis of magnetic resonance imaging data. It was designed by and is maintained by the scientific computing group at the National Institutes of Mental Health. It can do just about anything you ever wanted to with your MRI data.   and it will give you all the gory details about how it does those things. 
FSL was developed by and is supported by the Wellcome Centre for Integrative Neuroimaging at Oxford University. It's a great compilation of tools that are more user-friendly, but exhibits considerably bit less transparency than AFNI with regards to how it works. 
ANTs Advanced Normalization Tools was developed by the University of Pennsylvania Image Computing and Science lab. It does image registration, segmentation, bias correction, alignment, cortical thickness, and more. If you're serious about MRI, you should check out this set of tools.