I've been looking into computer algebra systems for some mathematical noodling that I'm doing. I'm rusty enough at calculus that they are a useful crutch, but if I get handy enough with them they could be useful in ways beyond my current problem. I'm interested mostly in doing symbolic manipulation and I've found that Maxima seems to be the free gold standard for what I'm interested in. However, I've ended up using a program called SpaceTime, because it seemed to have a lower threshold to get to useful results and because it has versions that run on my PC and on my iPhone. The PC version is free and the iPhone version is $20, which I haven't yet decided to pay, but isn't it wonderful that I can try it out for free?
There is an interesting anecdote or two here, illustrating why one might want to do computer algebra.