I don't know which country has most castles, as this depends on your definition of a castle, whether you count ruins as well, and whether you are looking for density of castles per area or overall number...and "fascinating" is also a very subjective expression...As you posted in Medieval History, you are probably interested in defensive castles, and not renaissance or baroque palaces.
In South Germany, there are many castles. Many of them are ruins, but still there is quite a number which survived - often not completely in the original state, but modified in later times.
Burg Eltz, an example of a castle with many preserved medieval structures.
Veste Coburg (like in Saxe-Coburg and Gotha, who today prefer the name of "Windsor"), an example of a castle with still many medieval structures, but also many later additions.
Burg Hohenzollern, ancestral seat of the Hohenzollern dynasty, an example of a castle with medieval origins, but almost completely rebuilt in the 19th century.
Neuschwanstein castle, the most famous castle with tourists, is fascinating, but nothing more than a substantiation of the wild dreams of a crazy 19th century king. There are many other castles, for example along the Rhine valley, and also in central Germany (Thuringia with the famous Wartburg, and the many castles of Saxony).
My personal favorite land of castles however is Tyrol. As Tyrol was the location of many important mountain passes crossing the Alps, many castles were built to protect these passes, or to make the passing people pay heavy tolls, or to even rob the voyagers and then retreat to one's castle...
The Haderburg in South Tyrol, high above the village of Salurn.
Schloss Tirol, the most famous castle in South Tyrol, ancestral seat of the counts of Tyrol.
Schloss Runkelstein, above the city of Bozen in South Tyrol.
[Source for all images: Wikipedia]