Let's start with the colored stones, which seem to be much more popular among royal brides than the rest of us common folk:
Sapphires
Left to Right: Diana, Princess of Wales; Tatiana Blatnik; Marie Chantal, Princess Pavlos; Princess Anne (from her first husband)
Rubies
Top Row, Left to Right: Crown Princess Mette-Marit and Queen Sonja (Sonja's originally belonged to King Harald's mother, and she gave it to Haakon when he proposed to Mette-Marit); Sarah, Duchess of York; Princess Mathilde; Crown Princess Mary
Bottom Row, Left to Right: Princess Diana of Orléans; Clotilde, Princess of Venice and Piedmont; Princess Alexandra, now Countess of Frederiksborg (from her first marriage to Prince Joachim); Princess Märtha Louise
Other and Multiple Colored Stones
Left to Right: Princess Marie (Joachim's second wife); Princess Máxima; Wallis, Duchess of Windsor
Diamonds, Small to Average Size
Left to Right: Princess Madeleine (it may have been given back now, but it was nice while it lasted); Crown Princess Victoria; Princess Alexia of Greece and Denmark; Princess Nathalie of Sayn-Wittgenstein-Berleberg; Lady Sarah Chatto
Diamonds, Climbing Up the Size Ladder
Left to Right: Queen Elizabeth (click here to read more about this ring); Sophie, Countess of Wessex; Autumn Philips; Princess Letizia; Queen Beatrix
Diamonds, Holy Crap Category
Top, Left to Right: Queen Margrethe; Princess Grace; Camilla, Duchess of Cornwall
Bottom, Left to Right: Crown Princess Sarah of Brunei; Princess Soraya of Iran; Queen Saleha of Brunei; Queen Paola of the Belgians
So, what's your verdict? My picks:
Best Royal Engagement Ring
Princess Grace
I'm a diamond girl myself. Goes with anything and everything you want to wear, you'll never tire of it. And as far as I'm concerned, a royal engagement ring should be huge. It's a fairy tale thing, you know? Grace's is perfect; impressively large without being as comical as Margrethe's, Soraya's and Saleha's, and the perfect emerald cut shape.
Worst Royal Engagement Ring
Princess Marie
Blech. Supposedly, Joachim wanted to echo the colors of the French flag for his French fiancé. Just buy her a souvenir flag instead, for heaven's sake. This is gaudy and clunky, and not at all befitting Marie, who has much more delicate features than this ring demands.
Catherine Middleton receives Diana, Princess of Wales' sapphire ring from Prince William.
Zara Phillips gets a custom-designed diamond ring from Mike Tindall.
Countess Stéphanie de Lannoy received this diamond number from Guillaume, the Hereditary Grand Duke of Luxembourg.
Tatiana Santo Domingo has been spotted in this large ring since her engagement to Andrea Casiraghi.
Princess Madeleine of Sweden received a diamond ring from Christopher O'Neill.
UPDATES
Some of the royal engagement rings that have popped up since this post was written:
