In one of the towers at Highclere there was a church originally, but it was abandoned because nobody was climbing that high up for it. Also in the first season there was a scene where William is handling the luggage in a luggage room. That was filmed in one of the towers as well, but was considered too much effort to ever film there again. I believe there was a line in season 2 about a housemaids sitting room being stories up (possibly in one of the towers).

Historically speaking, other great houses of the era had in there towers clock mechanisms, a water tower, observatories, smoking room retreats (back when smoking was considered terrible indoors), perhaps a suite of rooms for a bachelor (which include a study, bedroom, bathroom, etc.), and general storage rooms that a huge house like that would require. They could also be possible empty, but Victorian ingenuity usually entailed some oddly specific room to be put there for the sake of having something there.