With the exception of solving integrals, diff eqs, or other CAS things, is Wolfram Alpha particularly useful when you'd have google at your disposal? I would think no, but that's just my experience.
Who is downvoting this comment!? It's a non-inflammatory, relatively accurate portrayal of Alpha. WA does some things well (sure, more than just CAS) but at the end of the day its cool factor far exceeds its useful factor for the vast majority of people---especially because of several problems with its UI that have been discussed at length in the past.
But how often do people actually compute? The majority of all computer use is for information retrieval/display. If wolfram alpha had a spreadsheet interface then maybe people would use it, but once again right now there isn't that much that people compute.