Exploratory Testing
Scenario One I'm rewriting an ASP website into ASP.Net. It's going well. I can now run the two systems side by side, seeing what is different and what's the same. Over a finite site that seems just as good a test as having a specification.
Scenario Two On snother website I was asked to add a confirmation email when a new user registers. I've noticed a lot of errors on this page. My first guess was that this public page is falling prey to web crawlers. After all, my exploratory testing didn't make it fail. But I was wrong. Checking logs yesterday I found that the error was the confirmation email - a badly formed email address (why do users do this?) and it was throwing an error. It's fixed now.
Conclusion Exploring means opening your mind to come up with likely scenarios. Get it right, and its an effective use of time.