It seems that since the launch of WolframAlpha people are generally testing it rather than using it. Although, I'm willing to bet, there are people out there that are using this amazing service for doing actual research and are finding it altogether indispensable already.
Dave Winer tested it on a Friday night. He ran some pretty interesting tests ranging from a vanity search to queries about movies. His queries were interesting but I don't think they are inline with what WolframAlpha was built for. His searches were just that, searches. They weren't comparisons, questions, or equations of any kind. While WolframAlpha is perfectly capable of letting you know what 2001: A Space Odyssey is - it does a much better job at telling you how much money the movie made at the box office, or the weather the night the movie was released.
Amber Simmons decided to try to make WolframAlpha fail by asking it some questions that she's wondered about since childhood. Her results surprised her.
When I initially tested WolframAlpha it was immediately after I had watched the screencast explaining what WolframAlpha was built to do. I did a comparison search on Viddler and Brightcove, a search to figure out my ideal body weight, and one to figure out how many calories I'll burn running that 5K every other day.
The jury is still out on how I will use WolframAlpha but I do not underestimate its abilities nor it's teams abilities to adapt the tool for nearly anything you need. I'm very much looking forward to the future of this product.