Each Pope has his own style, but they are all teachers. Benedict XVI has a magnificent gift to be able to present complex ideas in a very understandable, articulate and eloquent manner.
I have a feeling that it would be incredible just to sit in his presence and listen to him talk about almost anything.
You and me both!
He seems an excellent teacher.
Before he became a bishop, he was a university professor. He is an academic at heart, a true scholar in the best sense of the word. He has tens of thousands of books and loves to read and write. While he was a Cardinal he entertained hopes of being able to retire to read and write books at his home in Germany near his brother, Georg. Alas, that did not come to pass. However, the role of Pope gives him an extraordinary opportunity to teach the entire world.
Benedict XVI also has the ability to beautifully craft his answers to different audiences. I am thinking of a public audience he gave to children who had received their First Communion within the past year. A handful of the new communicants were given the opportunity to ask him questions about the Sacrament of Communion. Their questions were pretty typical of young children. His answers were substantial yet he didn't talk down to them or over their heads.
I see NYer has already given you a link to the various communications of Benedict XVI during his pontificate (and a brief period before). If you are interested in reading some of the books he has written, you can find them at Ignatius Press, which publishes his books in English.