The R Project for Statistical Computing
If you conduct empirical studies you have to analyze your data. In many cases applications like MS Excel or Open Office Spreadsheet are enough, but sooner or later you get to the point when you need a professional statistics package. If you don't have access to commercial tools like Statistica, MATLAB or S-PLUS, the R package might be the best choice for you ...
I will not give you any tutorial concerning the R language here, because there are many good ones available all over the Internet. The one I would like to recommend you is available at the page Quick-R [2]. Each installation has also a built-in help and tutorial which both are extremely useful too. If you are looking for help concerning graphics and plots, visit R Graph Gallery [3].
The R package is available for nearly all popular operating systems (Windows, Linux, Mac OS). You can download it from the R project homepage [1]. The first good information is that R is GNU project and it is freely available to you :)
R itself is a different implementation of the S language, which was developed at Bell Laboratories. It has huge amount of statistical functions already implemented and there are also much more in external packages available on other sites. In other words if you need any statistical function, test etc. you can be almost sure that it is waiting for you in R. If you are really demanding user, you can write your own package and share it with the community.
I should make small remark here. Whenever you use a package (especially external) don't assume it is free of errors ;) It is good to compare results if you have any other tool available. On the other hand it usually happens that there are few similar ways of computing some statistics, performing tests etc., which can lead to slightly different results. All in all, you should keep that in mind while using R.
As I said before R is programming language that means two things: the worse one is that you will have to learn a new syntax, the better one is that you will be able to do the things you've always dreamed about while using Excel... and with only few lines of code :)
To sum it up. If you don't have money for any commercial statistcial tool and you like to perform non-typical analysis of data, R is a good choice for you!