On Friday the Spanish government approved an amendment to the decree of 6 November 1987 on royal titles, so that King Juan Carlos and Queen Sofía will retain the titles of King and Queen after his abdication. They will also retain the style of Majesty, but, interestingly, will rank after the descendants of the new King and Queen. This is, according to the government, done partly as a mark of respect for King Juan Carlos's and Queen Sofía's services to Spain, but also in keeping with historical precedents and customs in other monarchies.
Indeed I believe both King Carlos IV and Queen Isabel II retained their royal titles after their abdications. This is also how things have been done in Belgium and Luxembourg. Currently King Albert II of the Belgians, who abdicated in 2013, and Grand Duke Jean of Luxembourg, who abdicated in 2000, retain their titles, as did their parents, King Léopold III, who abdicated in 1951, and Grand Duchess Charlotte, who abdicated in 1964.
Britain and the Netherlands have chosen another solution. When King Edward VIII renounced the British crown in 1936 it was decided that his ceasing to be king meant that he reverted to being a prince, and he was granted the dukedom of Windsor in addition. Queen Wilhelmina of the Netherlands, who abdicated in 1948, argued that her abdication was constitutionally equal to her death and reverted to being Princess Wilhelmina. This precedent was followed by her daughter, Queen Juliana, when she abdicated in 1980, and again by her granddaughter, Queen Beatrix, who renounced the Dutch crown last year.