Hi Dragan,
Wow - no easy questions on this list
. Let me take a shot.
When it comes to data analysis, R's biggest competitors are Excel, SAS, IBM SPSS, and Stata. With the exception of R, all are proprietary. I use each regularly and each has strenghts and weaknesses compared with R and with each other. Let me know if you want me to go into them.
In the open source world, I am hard pressed to think of competitors. Nothing matches R's breadth of coverage or graphic capabilities. In addition to the wide array of built-in functions, there are thousands of user-contributed packages of functions easily available through
CRAN.
In the data mining space, there is a good list of free (though not necessarily open source) software available from
KDnuggets. Orange, RapidMiner, Rattle, TANAGRA, and Weka are popular.
In area of exploratory graphics,
MANET is well known. However, much of its functionality is now available in R through the iplots package.
A good general link for free statistical software is avaible from
StatPages.net. It is comprehensive, but some of the software is quite dated now.
If you are interested in Orange,
Red-R extends Orange to communicate with the R interpreter using the Python-R interface rpy. I have not worked with it.