Yesterday Elizabeth left a comment that brought an important piece of information to my attention. I tend to forget that other states have strict reporting laws when it comes to homeschooling. We happen to live in a state that has no reporting requirements. So, if you live in a state that has stricter laws and required paper trails, you can still do unit studies as your main style of learning, it will just require more documentation and possibly thinking outside of the box to get it done.
I was just rereading a book that I had about unit studies called "Unit Studies Made Easy" by Valerie Bendt. In part of the book she discusses how she keeps track of what her children have learned. She keeps a spiral notebook open with one page per child per day. On it she records all of their activities and classifies them into a typical subject of study. She makes note that she records things the family might do outside of typical school hours since those activities can certainly qualify as learning. For example, making a meal for a sick family could be classified as Home Ec, gardening time could fall under science, etc. This way she has documented evidence that her kids are studying and learning.
As just another example of how to set up a unit study, I would like to tell you about one that we did on Romantic Era composers. We obviously studied music, and in addition to that we covered history by learning about various composers. We mapped out where each of them lived, thus covering some geography. My oldest did research and wrote short reports on various composers. We also watched some movies that were related to certain composers, as well as learned to play their songs and listened to recordings of their music. When you think about it, it is fairly easy to cover a good deal of ground by taking a look at just one topic.
I'm not sure if I'll have time to post anymore before the conference, so I hope this has been helpful.