This video shows how you might use WolframAlpha in your classroom (click on the title to launch the video). You may also want to check out the educator section which includes lesson plan ideas, additional videos and more. Go to http://www.wolframalpha.com/educators/
Generally I find it is very reassuring to have it there - I don't freak out when I get stuck, because I know I can usually get some tips in my working out by dissecting a problem into manageable chunks and running those chunks (e.g. differentiation) through the engine. I can see how maths students at school would benefit from this backup/safety net/ like have a tutor check your work.
I think every maths student should know about it. (just like the Khan Academy!)