Yikes...strange symbols keep appearing on my article....
Let me try again:

Yesterday, I had to attend a meeting at work (we are in the middle of our summer vacation, but trying to get a head start on new things going on in our school district...long, boring story). We met a new co-worker, a teacher coming to us from another school who will be with my grade level...she seems very friendly, and is eager to join us.

Anyway, after a long morning full of work, we decided to stop for lunch. As we were being driving to our destination, the topic of family and children was brought up...After a third coworker finished talking about her twin sons, I nonchalantly asked my new co-worker, “Rita, do you have kids?”. She paused for a bit, and then replied, “I have a hard time answering this question...”
I then heard a sniffle and an attempt to suppress a soft cry. “I cry whenever someone asks me this question. Let’s just say that I have two little ones waiting for me up in heaven.” I of course, was at a loss for words for a few seconds...
I obviously brought up something very painful to her...I felt awful, just awful. I did eventually manage to offer my condolences, to which she replied, “Oh, it’s alright. This is something I have never shared with any of my co-workers before.” The subject was dropped, and we went on to have a nice, long lunch.

This incident got me thinking: Is this a rude and unnecessary thing to ask? Is this type of questions along the likes of “So when are you getting married?
or “How old are you?” Sigh...maybe I just should have waited for her to bring it up on her own.

InBloom, it sounds to me like you asked a perfectly innocent question during a conversation.
I think most, if not all, of us have "buttons" or issues that are painful for us to deal with, and I think your
friend handled it the best way she was capable of at the time, and you too said exactly the right thing to her.
It's difficult to know what to talk about these days with even our closest friends, and family. I've been on both
sides of "this fence", this dilema that happens when we touch on a subject or ask a question and it was
an :owie" for someone, not to downplay the importance of her feelings by saying "owie". That's one of my
expressions.
It would be great if someone came up with a list of questions to or not ask of others. A couple of years ago I attended
the "yearly summer get aquainted" picnic our managers threw every August to help the residents get to know who is living in our complex.
A new couple that had just moved in seemed to me to be asking ALOT of questions and it turned out she's a psycologist
and he's a shrink. They didn't know me at all, that I had lived there 7 years, and what I'm coping with, and when he asked me "what do you do for a living?"
I replied "as little as humanly possible". It's difficult for me to deal with the disabilities I have and when I get asked that question, I have
to try and joke and change the subject.
Over all I think saying a simple "oh I'm sorry" and then moving on to something else is all anyone can do if we breach ediquette unknowingly.
and I just wrote a book!!! gosh.

Here in Korea it is normal to ask a lot of questions on first meeting someone, "How old are you?" "Are you married?" Even asking how much someone earns is not considered particularly rude.

The reason is that this is a highly status conscious society and people 'need' this information to know how to relate to the person they have just met (are they 'senior' or 'junior' to me?)In fact without this information further conversation becomes difficult. In the Korean language you have to add endings to verbs which express the perceived status of the person you're talking to and even sometimes the status of the person or thing you are talking about.

In the west, as your post shows, we tend to worry a lot more about 'appropriate' and 'inappropriate' questions. For my two cents, having been grilled so often by Koreans on the minutiae of my private life ("Not married? why not!?") I can't see anything at all intrusive in your well-meant and kind curiosity.

'In the west, as your post shows, we tend to worry a lot more about 'appropriate' and 'inappropriate' questions.'
Perhaps so, but if we stopped to consider the potential risks inherent in all the possible answers to every question we asked, the art of conversation (and thus meaningful engagement with other members of the species) would die out altogether. You asked a completely innocent question, with no hidden agenda or intention to cause pain. That your colleague was upset by it doesn't reflect badly on you. I can't speak specifically for her, but in my experience, people are far more likely to appreciate such enquiries than not. They give them the opportunity to be open and honest, to share their experiences, rather than feeling they have to hide something of themselves away from the world.

Your question was innocent.  There was no way for you to know.  I am often asdked that question, and fortunately mine are all alive and healthy.  It would have been inappropriate only if you knew she had children, and they were dead, and you asked her how they died.  But asking about children is not inappropriate, but sometimes very sensitive.

Thanks for your replies, everyone...Saw her today and everything was great. I knew
that it was not a horrible question, but I just felt bad that it brought back painful memories for her.