Everyone who's anyone is doin it. R is the statistical software used by most academic statisticians. This means that if you go to a statistician for help with your data, you'll be able to understand their help! It also means that the support network is unparalleled. For almost any question you have, someone else has already asked it and had it answered in a clear and reproducible way. Check it out here.
Reproducible research. Using R (especially keeping R scripts) allows us to do reproducible research. You can go back at any time and reproduce exactly what you did 5 months (or years, or whatever!) ago to get that one graph. It also allows other researchers to follow the steps that you've taken to analyze the data.
R is open-source. This means it's free to use. More importantly, it means that there is a large community of R users who are regularly improving R. It's only ever going to get more useful!
It's platform independent. You can use R in Windows and Linux/Mac.
R is a programming language. As a programming language, R gives you flexibility to create new functions for data analysis and visualization that fit your own needs. As a part of the R community, you can then share your functions with everyone else and help make R even better!.
Beautiful evidence. The graphics are beautiful. R gives you a lot of control over your data visualization.
If you're interested in more tutorials (which I highly recommend!), there's a nice interactive online one at Try R Codeschool. RStudio has developed a package called swirl, which is a tutorial that runs in the command line of RStudio (great for learning R in the context of RStudio!). Joe Fruehwald's Study group for R is a great resource for R for linguistic data.