What's in a Name?
Once we had a new Pope (and the crime sprees and rioting of directionless Catholics subsided), several of my non-Catholic friends began asking why this German dude went with Benedict XVI. Why do any Pope's take new names? What's wrong with "Pope Ratzinger?" Well, I had no idea either, so I asked my priest (who's really a monsignor, so I'm confident he knows his stuff).
The basic answer is that Popes consider their election as a new beginning, a new chapter of their lives. It's not unheard of for people take new names as they begin new journeys, especially spiritual (although the only other high-profile recent example of this I can think of would be Prince/the Artist Formerly Known as Prince/Wait -- Now I'm Prince Again). This practice in fact goes all the way back to the Apostles when Simon became known as Peter. (Although, if I remember correctly, Jesus told him that he was to be known as Peter — it wasn't Simon's decision. Then Jesus went on to call him Simon Peter sometimes, further confusing the issue. Correct me if I'm wrong here.) If you were confirmed into your faith, think back to the ceremony. Were you asked to pick a confirmation name? It's not all that uncommon for Christians or even other religions to do this.
Anyway, you have a new beginning. So how do Popes pick their new name? Well, there's nothing stopping them from picking a unique name (personally, I can't wait for Pope Steve), but they often choose the name of a previous Pope to honor him and/or his legacy. In fact, Pope John Paul II took his name to honor Pope John Paul I, who died after only 33 days in the papacy. JPI was the first double-named Pope, taking his names from the previous pontiffs, Pope John XXIII and Pope Paul VI. (Thanks, Wikipedia!)
Pope Benedict XVI probably took that name to honor the peaceful legacy of Benedict XV, and perhaps he also hoped to soften his hard-line conservative image by choosing the name of a more moderate Pope.
So there you have it.