United Kingdom
HM the Queen - English and French
HRH the Duke of Edinburgh - English, French, and possibly some German
HRH the Prince of Wales - English and Welsh
HRH the Princess Royal - English and possibly French
Sweden
HM the King - Swedish and English
HM the Queen - Swedish, English, German, French, Spanish, Portuguese, and I believe sign language, but I am not positive.
Norway
HM the King - Norwegian and English
HM the Queen - Norwegian and English
Denmark
HM the Queen - Danish, English, Swedish, German, and French
HRH Prince Henrik - French, Danish, English, Vietnamese, and Chinese
HRH Prince Frederik - Danish, English, French, and German
HRH Princess Mary - English and Danish
the Netherlands
HM the Queen - Dutch, German, French, English, and possibly Italian. It is said that she understands Spanish as well.
Belgium
HM the King - French, Dutch, German, and possibly English and Italian, although I do not know.
HM the Queen - Italian, French, German, English, and Spanish.
HM Queen Fabiola - Spanish, French, Dutch, German, English, and possibly Italian.
Luxembourg
HRH Grand Duke Jean - Luxembourgish, French, German, and English
HRH the Grand Duke - Luxembourgish, French, German, English and possibly Spanish
HRH the Grand Duchess - Spanish, Luxembourgish, French, and German
Spain
HM the King - Spanish, English, possibly French, and I read Catalan. He probably speaks some Portuguese and Italian as well.
HM the Queen - Greek, Spanish, English, French, and possibly German and Italian