The first is the wildly successful Freakonomics by Steven Levitt and Stephen Dubner. There really isn't a unifying theme to Freakonomics. The authors even admit this. But I found unifying ideas in these principles discussed throughout the book.
1.) Conventional wisdom is usually wrong. Sometimes you must look at things from an uncoventional manner to find the true story. Sometimes you must ask unconventional questions to discover the truth about everyday subjects. Conventional wisdom is lazy. Freakonomic thinking is challenging. This explains why very few actually challenge conventional wisdom.
2.) Incentives are the prime motivator for most human behavior. You want to know why people do the things they do? You want to alter negative behavior and encourage constructive behavior? Examine the incentives.
3.) Economics should be more than numbers and graphs. It should help explain human behavior and perhaps offer ideas on how to improve our lot in life. Freakonomics is fascinating and offers interesting insight into American life.
The second book on my reading list with an economic premise is "Banker to the Poor" by 2006 Nobel Prize winning economist Muhammad Yunus. This book deals with the success of the microcredit movement in Bangladesh. It has fascinating insights in to how to approach poverty in a pragmatic and successful way. I'll post more on it later.
So to me, to think freakonomically means to think in new and innovative ways. To examine issues from a different point of view and sometimes that means boiling things down to their essence. Simplicity in perspective is often an elegant and enlightening pathway to understanding.