I've been there several times! I used to live about a 4-hour drive away from that castle.
It is absolutely gorgeous! And not just the castle, but the whole region. Bavaria is one of my favorite places in the whole world, and I've traveled all over the globe. If I could pick any place to build my dream home and retire, Bavaria is very high on that list. King Ludwig II picked a perfect spot for his fairytale castle.
He wasn't smart about how he built it, though. His country was going broke and rather than deal with his subjects, he just fucked off to the corner of Bavaria to make a fantasy castle based on the works of his favorite composer, Richard Wagner.
He was so hated by his people for funneling all his money into this castle instead of helping them to survive, that one day he "mysteriously" drowned in a tiny little stream out back behind the castle. Construction on the castle stopped immediately and they turned it into a tourist attraction to generate money for the kingdom. The economy rebounded and it's been a tourist attraction ever since, so no one's officially lived there (the royal family had a summer home next door) and it's not 100% complete inside.
Still, it's a gorgeous castle and I highly recommend checking it out if you're in the area. The famous shot of the castle from the back/side is taken from a suspended foot bridge behind the castle. Definitely make the hike through the woods to see that view! The whole valley below the castle is beautiful to drive through as well.
Another interesting fact while we're on the subject. All the American stereotypes of Germany (beer, bratwurst, lederhosen, yodeling, etc.) is actually Bavarian culture, not German culture. Germans outside of Bavaria get really insulted if you bring up these stereotypes with them.
Bavaria has a very rich and interesting culture. They wanted to split off from Germany and become their own country once upon a time, but then Hitler decided to make their capital, Munich, into his headquarters for the Third Reich. Then the whole place was bombed to hell during WWII.
After the war, when Germany had to pay to rebuild Europe, most of the money came from Bavaria, which was an extremely rich region at the time. So they were bombed back to the stone age AND broke. Bavaria had to settle as a region of Germany instead of becoming their own independently wealthy country.