"What are your hobbies?", "What kind of music do you like?", etc., are quite annoying.
"Do you miss your family?" and "How come you speak so well our language?" (I don't live in my home country), are not exactly annoying, but, what the hell? Do people really expect any answer that won't be a lie (first question), or self-evident (second)?
But the question that really annoys the hell out of me is, when I start doing something late in the day, people come and asking me "You are starting this stuff now? At what time will you finish?". What the heck should I answer? If I say "I'll finish at 21:00 or 22:00 or whatever, the next question is typically "But why did you start so late?". If I tell them to leave me alone, it's always "I asked because I care, why do you have to be like that, etc". As for very lately, I found the correct answer ("Don't ask me this, I'm stressed already"), but, still, it bugs me.
One of few favourite questions asked by "friendly" strangers when I'm force to go to social events with my parents.
"So what high school do you go to?"
Just earlier this afternoon, my mother was going to places that offers private tutoring to ask about summer classes for my brother. I happened to be there and the darn man thought I need help with high school math despite numerous attempts by us saying it's for my brother...
It'd have to be "why aren't you seeing anyone?" / "why aren't you married?" This question practically asks itself at any sort of family gathering (when inevitably surrounded by siblings/cousins and spouses). Nobody even has to *say* it (although they do) for it to be uncomfortable. Ugh.