Wouldn't ask unless I was brainstorming or I genuinely thought something was up as in her expression of deep concern or sadness.
Don't think I'd ask it like "what your thinking" though.

I am a big believer in honesty, and I enjoy exchanging thoughts. So I am more than happy to give them my most honest answer. If someone asks that question, they should be ready for an honest answer. If my answer bothers them, then I know this date is a waste of time, and I will end it as soon as reasonably possible. If a significant other is bothered by my response, I will try to find out what is really bothering them...... it has to be out of the ordinary behavior for them, or they never would have made it to significant other status with me.

I guess it depends upon the level of intimacy I have with the person asking the question, and I've probably annoyed some people with the variation of it: "What's up?"

If it's someone close who is asking and I don't want to share, I say I'm just disappearing into my head a bit and that ends it. I can't fault a loved one for wanting to be with me. That said, when my late husband I and became engaged and family asked how we knew this was the right match, our answer was the same, "I can be alone in the same room with him/her and it doesn't drive me crazy."

Bugs me too. Maybe they should start the conversation with what they're thinking about...

How about "wanna talk?"
"Sure"
"What do you want to talk about?"
"You asked me if I wanted to talk, what's on your mind?"
Endless circle.

I admit to,after hours of silence, sometimes asking my spouse this question and he will say “Nothing” but rather than being evasive he swears his mind was genuinely blank. Blank. Whereas at least I have a stream of thought while quiet.

I've gotten this question but mostly from someone I was dating. I understood that it probably meant she was looking for some confirmation that I wasn't somewhere else in my head rather than with her in that moment and that she was probably hoping that I would be a little more open/vulnerable in our relationship, but it always caught me off-guard. Generally what I was thinking about at the time was just something general or some anxiety from the past that had randomly come up (happens to me all the time), but it doesn't necessarily mean this is information that I felt is even worthy of sharing. Other times my mind is a complete blank and then I'm left saying, "Oh nothing," to which she would seem suspicious of what I was REALLY thinking or wonder why I apparently have nothing going on in my head.

I live most of the time in Spain at the moment and they hate silence here. They will talk non-stop about nothing rather than let silence fall. It is very wearing. I think people who ask that question may also be uneasy with silence.

Somebody at work asked me that question and I answered "Do nymphomaniacs get repetitive motion injuries?". And nobody has asked me that question since.

I think that a lot of people who are not introverted are uneasy with the relative silence of introverts. They assume something is not right. They may think there is something wrong between you or they just think there is something troubling you. Then there are all those people who think you need help opening up.

If the other person has been waiting for you to say something, they probably DO wonder what you are thinking about. If you give them the "if i wanted to share what i was thinking..." line, that WOULD be off-putting. Why would you be spending time with them if you aren't willing to share (at least some of) your thoughts?

You can honestly say, " I was trying to think about something to say next." Or you can LIE; come up with a couple of white lies to smooth over uncomfortable pauses. "I was thinking about how beautiful your eyes are."

I don't think they are trying to be intrusive. Yes, it may indicate a little insecurity on their part, but as introverts, aren't WE insecure about social interaction? And shouldn't we therefore have some empathy for others who might feel the same way?

It depends on who is doing the asking and what is the setting! Between intimates, in together time, my perception is that it may be an invitation to speak intimately. Or to engage intimately.

Between enemies - it might be an invitation to have it out!

Anyway, it is clear that my thinking is different than the majority on here. Oh well! So it goes.

Just sitting here plotting a night of rape, plunder, and pillage. What are you thinking about?

I hate it more when they tell you what they think you are thinking and hold their assumptions against you. This is a no win situation

It seems intrusive, and puts me on the spot. Don't like it.

Yes, my thoughts are private, no? And I hate when people ask what am I doing (by text or on the phone) or what plans do I have for the weekend. But that's usually because they want to tell me what fun plans they have while I am planning to do laundry and watch Simpsons with my kid.

I don't like it either. That always feels like an invasion of my privacy.

That question annoys the shit out of me. I always sidestep when I get it. As you said, if I wanted to share my thoughts, I would do so.

Yes it is bad when people ask me that, they act like I'm scheming something.