About the Name Windsor 
The royal family has little use for last names - after all, everyone knows who they are. 
Princess Diana  did not take back her maiden name, Spencer, after her divorce; she  continued to be known simply as "Diana." The Queen signs official  documents "Elizabeth R." The R stands for Regina, which means "queen."  (Regina is not one of her given names; she was baptised Elizabeth  Alexandra Mary.)
But the royal family does have a last name, and they do use it from time to time. This wasn't always the case. 
Queen Victoria's  husband, Prince Albert, was a member of the House of Saxe-Coburg-Gotha,  so her descendants were part of that dynasty. This, however, was not  the family's last name. They didn't have one, because they didn't need  one, so they didn't worry about it. Experts later worried about it for  them and decided their name was probably "Witten" (or maybe even  Wipper).
The royal family's official name, or lack thereof, became a problem  during World War I, when people began to mutter that Saxe-Coburg-Gotha  sounded far too German. King George V and his family needed a new,  English-sounding name. After considering everything from Plantagenet to  Tudor-Stuart to simply England, the king and his advisors chose the name  Windsor.
To this day, the British royal family is known as the House of  Windsor. When Princess Elizabeth (the current queen) served as a  subaltern in the Auxiliary Territorial Service during World War II, she  was called "Elizabeth Windsor." Elizabeth married Prince Philip of  Greece, whose family name was Mountbatten, and eventually she decreed  that most of her descendants would be called Mountbatten-Windsor.  Princess Anne used this name in 1973 when she married Captain Mark  Phillips.
However, according to statements made by the queen, it appears that  Windsor is still the official family name for any British royal who is  styled "Royal Highness." The queen's youngest son, Prince Edward, the  Earl of Wessex, has used the name Edward Windsor professionally. His  wife, the Countess of Wessex, has been known professionally as Sophie  Wessex.
The Order of Succession
The queen has given her approval for Parliament to consider a law  that would give royal daughters the right to inherit the throne before  their younger brothers. Under current law, Prince Andrew and Prince  Edward (and their children) rank ahead of their older sister, Princess  Anne, in the line of sucession. If the law changes, Anne will be fourth  in line to the throne. Prince Charles, as the queen's eldest child, will  remain heir to the throne.
The current order of succession
Prince Charles, the Prince of Wales
Prince William
Prince Harry
Prince Andrew, Duke of York
Princess Beatrice
Princess Eugenie
Prince Edward, Earl of Wessex
James Windsor, Viscount Severn
Lady Louise Windsor
Princess Anne, the Princess Royal
Peter Phillips
Savannah Phillips
Zara Phillips
Catholics and the Act of Settlement
The 1701 Act of Settlement made it illegal for a Roman Catholic, or  anyone married to a Roman Catholic, to inherit the throne. (Note: It has  been rumored that Prince Charles's second wife, the Duchess of  Cornwall, is Catholic, but this is not true.)
Royal Palaces
The royal family uses, but does not own, Buckingham Palace,  Kensington Palace, St James's Palace, Hampton Court, Windsor Castle and  other residences. Balmoral and Sandringham are the queen's personal  property.
The Firm: The Troubled Life of the House of Windsor  by Penny Junor. This book promises an in-depth look at how the royal  family really operates and how they behave behind closed doors.
The Women of Windsor: Their Power, Privilege & Passions  by Catherine Whitney. Examines the lives of Britain's Queen Elizabeth  II, the Queen Mother, Princess Margaret, and Princess Anne.
Wives of the Kings of England: From Hanover to Windsor by Mark Hichens. Discusses Queen Alexandra, Queen Mary, the Duchess of Windsor, the Queen Mother, and others.
The British Monarchy for Dummies by Philip Wilkinson. Explains the origins of the monarchy, how it works, what the royals do all day, and more.
Britain's Royal Heritage: An A to Z of the Monarchy by Mark Alexander. Contains more than 2,000 entries on topics such as Maundy Money and the Coronation Ceremony.
On Royalty: A Very Polite Inquiry Into Some Strangely Related Families  by Jeremy Paxman. With a mixture of popular history, direct reportage,  and funny anecdotes, the author examines how the role of Britain's head  of state has changed over the years.
The Decline and Fall of the House of Windsor  by Donald Spoto. Excellent introduction to the personalities and events  that shaped the Windsor dynasty, from the days of Queen Victoria to the  1990s. Despite the title, the author is not unsympathetic to his  subjects. Out of print, but available from Alibris.
Confessions of a Fake Sheik: "The King of the Sting" Reveals All by Mazher Mahmood. A journalist who poses as a wealthy sheikh talks about his encounters with famous people, including royals.
Living Off the State: A Critical Guide to Royal Finance  by Jon Temple. A detailed examination of the official finances of the  British monarch and leading members of the royal family. Examines the  Duchies of Cornwall and Lancaster; the Civil List; housing for leading  royals; the Royal Collection; and more.
Marcus Adams: Royal Photographer  by Lisa Heighway. Marcus Adams took his first portraits of future Queen  Elizabeth II in 1926, and he continued to photograph the royals  regularly until 1956. This comprehensive collection of his royal  portraits includes many previously unpublished images.
The Royal Scrapbook  by Robert Opie. Over 1,000 images illustrating more than 100 years of  royal events, beginning with Queen Victoria's Diamond Jubilee and ending  with Queen Elizabeth II's Golden Jubilee.
The Queen's Year: A Souvenir Album  by David Oakey. A season-by-season guide to the Queen's busy year,  illuminating the traditions behind many royal events. Illustrated with  new photos.
Magic Moments: The Greatest Royal Photographs of All Time  by Arthur Edwards. For thirty years, photographer Edwards has captured  memorable royal moments. This book contains his best color pictures and  unique stories.
Crowning Glory: The Merits of Monarchy  by Charles Neilson-Gattey. Argues that monarchy is a stabilizing force,  and explains how the concept of a constitutional monarch emerged and  how monarchs since Queen Victoria have played that role.
The End of the House of Windsor: Birth of a British Republic  by Stephen Haseler. Is the British monarchy an absurd anachronism or  the lynchpin of the nation state? This controversial book argues that,  as a result of recent scandals, a British republic is now inevitable.
War of the Windsors: A Century of Unconstitutional Monarchy  by Lynn Picknett, Clive Prince, and Stephen Prior. Examines the battle  for power in the modern British royal family. Topics include the  abdication of Edward VIII, the cover-up of royal financial scandals, and  the use of euthanasia on royals.
God Save the Queen? Monarchy and the Truth About the Windsors  by Johann Hari. The author says the royal family's members have been  broken and destroyed by the institution they were born into.
God Save the Queen: The Spiritual Dimension of Monarchy  by Ian Bradley. Explores the spiritual dimension of monarchy in  historical and contemporary times, and the debate on the future of the  British monarchy. Out of print, but available from Alibris.
Down With the Crown by Antony Taylor. British anti-monarchism and debates about royalty since 1790.
The Monarchy and the Constitution  by Vernon Bogdanor. English constitutional history and theory. The  author makes a case for the positive role that monarchy plays in modern  democratic politics.
King and Country: Monarchy and the Future of King Charles III  by Robert Blackburn. Unravels the tangled relationship between crown  and state in Great Britain, examining how a monarchy can work in a  democracy, the political powers of a British monarch and the nature of  the royal prerogative, the case for republicanism, and the future of the  monarchy.
The Nature of the Crown: A Legal and Political Analysis edited by Maurice Sunkin and Sebastian Payne. Essays about the monarchy and constitutional law in Great Britain.
The Constitutional History of England by Henry Hallam. From the accession of Henry VII to the death of George II.
The Executive in the Constitution: Structure, Autonomy, and Internal Control by Alan Page and Terence Daintith.
Honours and Rewards in the British Empire and Commonwealth (2 Volume Set) by Anthony N. Pamm.
Symbol and Privilege: The Ritual Context of British Royalty by Ilse Hayden. Customs, rites and ceremonies of British royalty. Out of print, but available from Alibris.
The Princess Royal by John Parker. A 1989 biography of Queen Elizabeth II's only daughter. Out of print, but available from Alibris.
Riding Through My Life  by HRH The Princess Royal. Princess Anne's own account of how riding  has benefited her life, from her first tiny pony through becoming  European Champion in the dangerous sport of Three-Day Eventing, and  representing Britain in the Olympic Games. From Alibris.
Anne: Portrait of a Princess  by Judith Campbell. About the events, joys, and sorrows of childhood  and life at school which formed Princess Anne's strong character.  Published in 1970. From Alibris.
Anne and the Princesses Royal by Helen Cathcart. A book about the position of Princess Royal through the ages as well as about Princess Anne. From Alibris.
Zara Phillips: A Revealing Portrait of a World Champion  by Brian Hoey. The only daughter of Princess Anne, Zara Phillips is  known as a royal rebel. This book looks beyond the public image to  reveal the real Zara with anecdotes and quotes from those who know her.
Out of the Shadows: The Richard Johnson Story  by Richard Johnson and Alan Lee. Autobiography of Richard Johnson, one  of Britain's leading National Hunt jockeys and the former boyfriend of  Princess Anne's daughter, Zara Phillips. Available from AbeBooks.
Edward Windsor, Royal Enigma by Wendy Leigh. What is Prince Edward really like? Find out! This biography is out of print, but available from Alibris.
Sophie's Kiss: The True Love Story of Prince Edward and Sophie Rhys-Jones  by Garth Gibbs and Sean M. Smith. The little-known details of the  romance between Queen Elizabeth's youngest son and the woman he  eventually married. Out of print, but available from Alibris.
Edward Wessex's Crown and Country: A Personal Guide to Royal London  by Prince Edward. The prince takes the reader on a tour through the  history of London's royal palaces. This is the companion book to the PBS  series (for which scroll down to the 
video section).
Princess Margaret: A Life Unravelled  by Tim Heald. A biography based on unprecedented access to the Royal  Archives and those closest to Princess Margaret, including her  ex-husband, Lord Snowdon, and her son, Lord Linley.
Margaret: The Last Real Princess by Noel Botham. Biography of Queen Elizabeth II's unconventional younger sister.
Princess Margaret: A Life of Contrasts by Christopher Warwick. Authorized biography. Available from Alibris.