Here is another library I would like to see one day: the Admont Abbey Library.
The Admont Abbey is a benedictine monastery located in Admont, Austria. According to Wikipedia, it contains the largest monastic library in the world and also has a "long-established scientific collection."
The Admont Abbey was founded in 1074. In April of 1865, a fire destroyed most of the monastery. Most of the monastic archives burned, but the library was saved. Reconstruction was completed in 1890.
The Admont Abbey contains 70,000 volumes and hundreds of manuscripts. I won't be able to check any books out of this library, but it sure would be great to see!
Have you got a great library to add to my list?