I don't feel like my T has asked me anything that was too personal...I usually bring up the really personal things because I need to work them out.
I find my T is very open, I don't ask her personal questions though, one time she was running late and when she came I just said I hope everything is okay, she replied that it was and that she had to take care of her puppy.
Sometimes she'll share things about herself without me asking, like when we talk about my childhood she'll discuss something she observes in her children and relate it to what we are talking about...another time I mentioned I love Dave Matthews Band and she said she liked them too...another time we were discussing my weight issues and she shared a book with me that helped her lose weight...so I like that she shares those little things with me, it makes me feel more comfortable.