Two of the most beautiful castles in the world, in my humble opinion: Christian IV's 17th-century creations in Dutch Renaissance style.
I can't say that I consider them the most beautiful in the whole world, but they are really impressive, especially the collections inside : ).
Denmark is a fairy-tale country, it impressed more than all German and French castles, more than Louvre and other European cities and museums I've seen.
The funny thing is that in his infamous "An Account of Denmark, as it was in the Year 1692" the British ambassador to Denmark, Robert Molesworth, the later 1st Viscount Molesworth, writes that all Danes go on about how beautiful Frederiksborg is, not understanding that only Danes think so! :-) Now, I'm not Danish, but Norwegian, but of course the builder Christian IV was King of Norway too, so perhaps it's in our genes...
What "gets me" about these brick castles is the mix of domesticity, no doubt especially thanks to the Dutch brick style, and fairytale romance. They look just like fairytale castles are supposed to look like and yet look so cozy that you could imagine living there. I guess that might be a feature of Renaissance architecture everywhere, because of it's humanist ideals: English Tudor architecture and especially the French Loire châteaux, of whom they are a perfect Northern counterpart. But of course when it comes to Northern adaptions of palatial Baroque, Russia rules!
BTW the Dutch Renaissance style became known as "Christian IV style" in Denmark and became very popular, both for manors, town houses and public buildings, both in Christian IV's days and during its revival as a "national style" in the 19th century.