Since today is Alan Greenspan's last day in office, I thought it'd be fitting to offer a few good books if you want to read something about the Chairman. I'll suggest just two out of many, many options.
First, for a broad view of his life, try Justin Martin's Greenspan: The Man Behind Money. You'll learn all about his youth, his affiliation with Ayn Rand, his love of music, and his career before the Fed. While there is a discussion of his time as Chairman, this book is better at providing the wide view of Greenspan's life. It's not without its faults - it was written without the cooperation of the Chairman, so it's drawn from secondary sources and interviews with former colleagues and friends, but it's still worth reading.
Unfortunately for Martin, his book was released at the same time as Bob Woodward's attention- grabbing book on the same subject. If there is any good news for Martin, it's that the books are highly complementary. Bob Woodward's Maestro deals in depth with the subject's time at the Fed and gives little attention to the prior periods. Hence there is a nice synergy between these books.
Robert Kuttner offers a less sanguine, but still generally good review of both books, if you want another opinion.
This is a great time to be covering Fed policy. Greg Ip had a very long, detailed look at the Federal Reserve in yesterday's WSJ, and there are op-eds running all week in the same paper. Robert Barro wrote yesterday's column and Milton Friedman did today's. If you have access you should check out all the coverage.
If you want more background on the Federal Reserve, they publish a very useful guide entitled The Federal Reserve System: Purposes & Functions. A free online version is available here. If you want a hard copy you can order through the NY Fed website (it's free.)