This is a difficult one. I really should be interested in everything, but in practice my interests turn out to be quite restricted. Usually I'm reading something for a very specific reason, to answer a very specific question, rather than being motivated by some diffuse notion of intellectual curiosity. For example, I want to know how scholars have defined the "counter-reformation." The material is as interesting as anything else, but what really interests me is one specific thing about it. So for me intellectual curiosity is very goal driven and guided.
On the other hand, I always allow for a certain randomness too. I read scholarly articles totally outside my field--at least the first few pages. I let my mind wander. Usually when I am in an intense work mode everything I read ends up helping me think about the project I am now working on--even totally irrelevant things.