From other cartoons and following on the twitter-sphere, you may have noticed I like exploratory testing. This testing is not a technique but an approach, a mind-set to testing, it's often contrasted to scripted testing but it's not as simple as saying they are opposites.
At my last two work places, I've introduced a more exploratory style of testing, but the fact is they were already doing it without realising. What I introduced is making the exploratory testing more visible and manageable so clients could see the testing that was performed.
The major reason I like exploratory testing approach is that I believe it is a more natural style of testing. With scripted testing, especially the scripts which are highly detailed, the tester has to follow the script when executing them. By doing this, they may miss out on other bugs in the software since the script does not require the tester to check for this. This is specially the case for lay out and usability issues. Issues which in the past may not have been business critical but are now increasing becoming so. If you have an awkward, unintuitive software application, users will be turned off by it and look for alternatives. With good exploratory testing, the tester is well equipped and use heuristics or guides to remind them of areas to look at.
Cem Kaner originally came up with the exploratory testing term and James Bach has developed the approach and provides training to develop exploratory testing skills. One heuristic that has triggered many bug finds is the "that's funny" heuristic. If you are ever using or testing an application and you notice something strange or you have a gut feeling something isn't quite right, then keep searching, you might find a bug!