Root is good, but I do get 'segmentation violation' errors a lot, accompanied by a core dump. It is often totally untraceable. I wouldn't say it's a "steaming pile if s**t" like the poster below me, by any means. I *RARELY* use the interpreter though, it might actually be a "steaming pile if s**t". But you can use the libraries right in your own C++, and some of the classes are truly great. Great histogramming, really easy to do graphing, easy function fitting (user defined as well as pre-canned functions), integrals, derivatives, you name it. The graphing is quite god. There is a Qt plugin for it too, so you can draw right on a Qt canvas. There is also a comprehensive python wrapper that comes with it, so you could do a PyQt-root analysis if you want, you can set it up kind of like an Igor experiment. It's actually really worth learning if you are a physicist, you'd be at a disadvantage if you didn't.
Qtiplot? Ehhh.. klunky, I lose patience every time I try to learn it.