You can get an excellent sense of the site's search abilities by watching this 13 minute video overview of Wolfram Alpha.
But if you don't have 13 minutes to spare, here's the skinny: For many natural language queries, Wolfram Alpha is game-changingly good. After reading our recent Guy Vs. Guy debating the use of cell phones in cars, you might want to do your own research. Ask "auto accidents in US" and you don't get a list of links, you get "45,077 deaths per year."
On the other hand, there's a lot I haven't been able to do with Wolfram yet. Based on our Guy Vs. Guy on the virtues of shutting down PCs at night, I wanted to see if Wolfram Alpha could tell me about the energy wasted by leaving computers on 24/7. I wasn't able to find a query that Wolfram could make sense of. (If you can formulate a meaningful query on this subject, let me know in the comments!)
But there's so much here to love -- especially for research. Enter two similar things (like MSFT APPL, apple pear, or U.S. England) and you'll get side-by-side comparisons of their most relevant attributes. Enter math equations -- even calculus -- and get an instant solution. You can even find out the weather on a specific date in the past.
Wolfram Alpha has a lot of promise, but right now one of the mainstream search engines (like Google or Bing) is going to get you what you need to know more effectively. For specific tasks, such as doing math or retrieving and compiling data from online databases, Wolfram is what the future of the Internet looks like. Have you tried Wolfram? I'd love to hear your experiences.