Yes, there is such a thing as too many questions.
My INFJ friend has a way of asking a lot of questions that almost feels accusatory when I don't know where she's leading. Maybe it's her direct style, or the fact that she's the only one that knows why she's asking. I get very defensive in situations like that, even though I know I've done nothing wrong!
I'm willing to answer lots of questions when it comes to a subject I'm interested in. In the classroom, for example, I take it as a sign of interest, and i like the challenge of answering students' questions to their satisfaction. It also helps me find holes in my lectures/explanations.
In my off-time, I don't mind if you ask me questions about my work or an interesting topic, but if it goes on and on, after a while, I'm going to get tired and/or bored, and hope for a subject change.
Another thing--some people rely entirely on other human beings for their knowledge when they could look it up themselves. That bugs the crap out of me. Don't ask me a zillion questions because you're too lazy to google it or go to the library.