Wolfram Alpha might be the most advanced piece of web technology nobody needs.
I expect Wolfram alpha has done a lot to drive sales of mathematica.
There was one time it worked for me, when I had to compute the derivative of a Lennard-Jones potential function. Even though it gave me a lot of different answers of the same formula written in complex different ways. I just remembered Mathematica has a Simplify function, maybe that would have worked in WA too.
Entering one's birthday and finding out how many weeks or days you lived is kind of fun.
For general calculations and unit conversions I prefer to use Google Calculator, for the simple fact that the page loads much quicker.
Its an amazing resource if you need what it has. So I assume as it keeps expanding I'll use it more and more.
Sometimes it works quite well; other times it's completely unable to parse the input and come up with any kind of answer, no matter how many times you rephrase the query.
As you can see, the queries can sometimes get rather tricky, but that is fun stuff. Also, it's a super-useful calculator.
</sarcasm>
That strongly suggests somebody do need it.
* Go beyond Alpha's capabilities in home use
* See the need for full-on Mathematica
* Are dedicated enough to make full use of it
* Don't already have access to full-on Mathematica somehow (work/uni computer, etc)
* Can't buy a student license ($140)
* Really wants to spend $300 on it.
Hm, how will I ever figure all that out? :)