Mathematica, Maple and Matlab are the 3 major programs. To say which one is better is a rather pointless argument, each has their own strength. However they are expensive.
There was a free graphing tool I've tried before...it is quite suitable for the HSC syllabus, although I personally use one of the major programs since I need some of the more powerful functions. However I do not remember its name. I'll try and find it for you.
They don't really help that much, just that it allows you to check the answer. As for the major ones they can be used to integrate/differentiate tricky/tedious problems, calculator beyond 15 significant figures, etc. So not really that useful in the HSC.