Neuschwanstein / Hohenschwangau
Neuschwanstein / Hohenschwangau are not really medieval castles, but are here anyhow because of the fame they have received over the years.

Neuschwanstein was the brainchild of King Ludwig II (1845-86) of Bavaria.  Nicknamed "Verucht Ludwig" by his detractors, Ludwig actually gave Bavaria numerous treasures now used as tourist traps!  Yet, Ludwig virtually bankrupted the Bavaian treasury to build his castles.  The son of Maximillian II, Ludwig patronized Richard Wagner and the Nordic themes of his operas.  These themes became enshrined within his castles.  Ludwig also supported Prussia in its war against France in 1870, helping to bring Bavaria into the new empire.  Due to his financial excesses he was declared insane and drowned while swimming in the Starnberger Lake.  Some claim he killed himself and others claim it was an accident.  Of course, some contend he was murdered to get him out of  the way.
Neuschwanstein was started in 1869 and was designed as a secluded retreat for Ludwig.  It was almost finished in 1886 when he was declared insane.  He had also been in the process of building such castles as Linderhof and Herrenchiemsee (a copy of the Versailles Palace in France). 

As can be seen in the profile photos, Neuschwanstein was designed in the shape of a swan (Neuschwanstein=New Swan of Stone).  Because of the motif of the castle and his patronage of Wagner, Ludwig was popularly known as the Swan King.  The castle rests on a rock mound and is actually quite difficult to access.  Concurrently, it has little use in an era of modern weaponry except as an ornament.
Below and below right, a shot of the side of the castle taken from the Maria Brucke that spans a gorge behind the castle.  Note in the detail that someone (from the center of the left photo) is currently engaged in taken their own photo towards the bridge!
Above, a nice view of the castle from the flatlands to the north.

Right, a view of the castle taken in 2005 from the mountain behind the castle.  The trail, if it can be called that, is arduous and not recommended for the light hiker.  After working the trail in 2005 and getting this shot, I encountered a couple from Seattle, WA.  As we came down, five older ladies (in their mid-50s+ were attempting to go up the lower portion of the trail, all dressed in casual flats meant for walking through the local town rather than any serious hiking.  I tried to disuade them, but they didn't understand German or English.  It turned out they were Italian!  The guy from Seattle knew some Spanish and managed to communicate some with them.  Nevertheless, they still would not listen at first and kept trying until they finally came to their senses and backed down.
Above left, a view of the castle from part of the trail at a location where Gudrun Bose fell to her death on 27 August 1966.  The location is very deceptive and apparently she leaned too far over and couldn't recover.  The fall was a good 100+ feet, well above the "coffin zone."  Above, a view of a better portion of the trail.  Some portions are virtually non-extant.  The trail leads to the cable car station in the valley that will take you to a mountain top behind the castle.

Left, two views of Hohenschwangau, a castle that ws originally an older medieval fortified house.  It was rebuilt by Maximllian II, Ludwig II's father, in the early 1800s.  It was used as a residence by the royal family of Bavaria off and on well into the 1950s.