I'm always amazed when I see the "Show Steps" button. You can learn a ton of things by just looking through the steps WA took to arrive at the result of a complicated derivative or integral.

I personally use it for tasks involving Linear Algebra, too, e.g. calculating eigenvalues and corresponding eigenvectors.

I also installed the Wolfram Alpha Chrome extension, which I use quite often and always comes in quite handy: http://www.wolframalpha.com/downloads.html