Royalties of all times had loved having portraits of themselves. The portraits are always very flattering to show the best of the royalty, bu that wasn't always the case. Some of the royal portraits are heinously unflattering and and ugly.
However, It's not always the artist's fault that the painting comes out looking pretty nightmarish, some royalty's looks are just slightly below average.
There are also artists throughout history who created intentionally bad portraits, as a means of criticizing a royal individual or family. Whether the result of bad artistry or royal inbreeding, these royal embarrassments are now our enjoyment.
King Charles II of Spain by Luca Giordano, 1693
Archduchess Maria Anna of Bavaria by an Unknown Artist, c. 1600
King Henry VIII by Peter Isselburg and Cornelis Metsys, 1646
King James II of Scotland by an Unknown Artist, 15th Century
Queen Elizabeth I of England by an Unknown Artist, 16th Century
British (English) School; Elizabeth I (1533-1603); National Trust, Tatton Park; http://www.artuk.org/artworks/elizabeth-i-15331603-131420
King Philip IV of Spain by Gaspar de Crayer, 1627-28
Queen Elizabeth I of England by an Unknown Artist, c. 1610
Prince Philip, Duke of Edinburgh, by Stuart Pearson Wright, 2004
King Ferdinand II of Spain by Michel Sittow, 15th/16th Century
King Ferdinand VII of Spain by Francisco Goya, 1815
Emperor Maximilian I of the Holy Roman Empire by Bernhard Strigel, 15th/16th Century
King Frederik VII of Denmark by an Unknown Artist, 19th Century
Mary, Queen of Scots, and James I by an Unknown Artist, 16th Century
Queen Caroline of the United Kingdom by James Lonsdale, 1820
Lonsdale, James; Caroline Amelia Elizabeth of Brunswick; National Portrait Gallery, London; http://www.artuk.org/artworks/caroline-amelia-elizabeth-of-brunswick-157214