The Brethren: Inside the Supreme Court by Bob Woodward and Scott Armstrong. This is the book that got me interested in the internal politics of the Supreme Court. It covers the first seven terms of the Burger Court. The Burger Court was in many ways a transitional court between the liberal Warren Court and the more conservative Rehnquist Court. Because of this, there are many strange decisions from the Court during this period. The accounts of the backroom dealings and politics among the Justices, the almost universal contempt for Chief Justice Burger, and the personalities of the Justices are all incredibly interesting. The newest edition has a different cover, but I'll always prefer the one on my first edition hardcover: old men in 1970's era suits. Snazzy.
A Court Divided: The Rehnquist Court and the Future of Constitutional Law by Mark Tushnet. I read this book earlier in the year for my American Constitutional History course. This is probably the most current book about the Supreme Court. Tushnet, a law professor, examines the important cases of the past 15 years and looks at the ideological differences among the Justices. His view is that the real split on the Rehnquist Court is not between conservatives and liberals, but between old school conservatives and Reagan-era ideological conservatives. The liberals only have five votes when those two conservative groups disagree on an issue. It's an interesting and readable book. Tushnet's biases aren't very hidden. He's no fan of Justice Scalia but heaps praise on Justice Thomas. One of Tushnet's major criticisms of Scalia is that his poison pen style of writing has alienated his colleagues, making it harder for Scalia to form majority coalitions.
The Tempting of America by Robert Bork. This book is really two books in one. The first half is devoted to a detailed examination of the history of Constitutional law and the Supreme Court. Bork analyzes each Court, looking at their controversial decisions, and tells the reader where the Justices got it wrong or right. He uses these examples as support for his favored judicial theory, originalism. This part of the book can be fairly dense and even had me looking up cases online and terms in Black's Law Dictionary. The second part of the book is the more readable and, in my opinion, more enjoyable. Here, Bork tells the story of his confirmation process. He gives the reader an insider's look at the entire ordeal, providing the kind of detail that only someone in his position could. It also shows the reader how smarter the Republicans have become since the Bork hearings. I wouldn't look for a repeat of history any time soon.
If you're interested in these books, I would recommend reading them in that order. Bork's book is easier to read if you have the kind of background that the first two books provide. There are a lot of legal terms and processes that you pick up just by reading the first two books. They really walk you through the whole world of the Court. Bork's not the handholding type. I would recommend having a decent legal knowledge base before jumping in with both feet.