Henry VIII wasn't really interested in affairs of state when he became king and he spent much time hunting, jousting and playing tennis. He left running the country in the hands of trusted advisors, chief of whom was Cardinal Wolsey, who was not only held various bishoprics but was also Lord Chancellor. In 1514 Wolsey purchased a property at Hampton Court and commenced extravagant building works, financed by Henry's largesse.

Henry owned many properties but none on the scale of Wolsey's Palace and as Henry grew older and more interested in affairs of state, he cast an avaricious eye on Hampton Court Palace, saying things like, "I must pay you very well, Cardinal" and "I wish I had a palace as beautiful as this" etc until Wolsey gave it to him. As Wolsey's star dimmed, Henry successively stripped him of his other properties, most notably taking York Place, Wolsey's London residence and giving it to Anne Boleyn. York Place was extensively renovated and later called the Palace of Whitehall.

Hampton Court Palace is really two palaces, that built by Cardinal Wolsey and improved by Henry and the second designed by Christopher Wren for co-regnants (and first cousins) William III and Mary II. The photo below shows where old meets new:

On the left is the Tudor building. If you zoom in you can see "ER 1568". I assume Elizabeth built or renovated this section. The right building was designed by Wren. Mary did no live to see it finished.

William and Mary wanted to demolish the Tudor Palace but fortunately they didn't have enough money. Henry built the last great medieval hall in England:

Henry and his retinue would move after weeks or months as the buildings became dirtier and more fetid. Henry owned 60 properties which he lived in from time to time, but Hampton Court Palace was his most sumptuous. He married his last wife, Catherine Parr, at Hampton Court. Jane Seymour gave birth to Edward VI here and died weeks later and Catherine Howard unsuccessfully ran though the room below to plead her case to Henry when accused of adultery. She was later beheaded.

Henry and Catherine of Aragon's initials had been painstakingly carved into various moldings and cornices and when he married Anne Boleyn, Henry directed that Catherine's initials be expunged and Anne's substituted. There are various places where tradesmen neglected to carry out Henry's directive, whether deliberately or not, I don't know.

Catherine had been a very popular queen because she was thoughtful, pious and kind. She bowed to the King in all but the "Great Matter" of a divorce. Anne, on the other hand, was haughty and vindictive and unable to stop herself from arguing with Henry. When she failed to produce a male heir and was put on trial for adultery, her father, Sir Thomas Boleyn and her very powerful uncle, the Duke of Norfolk did not defend her. The Duke of Norfolk was instrumental in bringing Anne to Henry's attention in the first place and he was one of those who found her guilty of treason (adultery) at the end. Norfolk was also instrumental in bringing another niece, Catherine Howard to Henry's attention. Norfolk carefully distanced himself from her when it became evident that Catherine had been granting favours to other men both before and after her marriage to Henry. The astonishing thing about Norfolk was that although he was central to two of Henry's most disastrous marriages, he survived and was only imprisoned for something else in 1546.

Thomas Cromwell was not so lucky. He engineered an arranged marriage between Henry and Anne of Cleves in January 1540. Henry's previous wives had been well-educated, cultivated and physically attractive. Each could converse in more than one language and dressed splendidly as befitted royalty. Anne of Cleves spoke only High Dutch, wore an abundance of dowdy clothing and could boast no accomplishments. The match was arranged, sight unseen by Henry. All Henry knew of his bride were the descriptions of others and a portrait painted by Hans Holbein the Younger. Henry fell in love with this portrait, finding Anne enchanting:

Nope, I don't get it either. Anyway, when Henry finally met Anne he was most disappointed and told his courtiers, "I like her not!" He was always kind and solicitous to her face, however, and married her because jilting her would have caused a diplomatic row.

The morning after the wedding, Thomas Cromwell nervously asked the King how he liked his new bride. Henry was very unhappy, saying, "she has evil smells about her". He engineered a divorce seven months later. It was the beginning of the end for Cromwell.

If you are interested in reading more about Henry and his wives, I recommend the following books: