Mostly as a means of rounding out the conversation and learning more about the person in question. Realistically, on very few occasions where I have asked, did the answer really spur the conversation to new heights.

I don't mind being asked what I do for a living. And anyone who is going to make assumptions about me is not going to be someone who is going to be compatible with me anyway.
I guess I ask the question as a small talk get-to-know-eachother type of question.

It's not something I would think to ask right away. Though if I were going to invite her to go outside to smoke some pot, it would be a good idea to make sure she's not a cop.

For me there are probably several reasons and Just Curious would be the least of the reasons. Please don't assume 'us' is men in this response, I'm trying to be gender neutral.

Initially its a conversation starter/"greaser" in that their reply can help us navigate to the next set of questions. Oh you're a botonist; clearly they are intelligent and like plants, thus we choose a line of questions that help them feel at ease. Helps us with determining shared experiences too.

Helps us determine social, economic, and educational compatibility; oh you're a pro-life attorney, well I work with Planned Parenthood maybe we won't work out. Obviously just because she has a PhD and he barely finished 8th grade doesn't make them incompatible, but the question helps determine how much we each have to put into this relationship.

To see how much you like doing what you're doing or do you have bigger plans than what you're doing.

Out of respect for the idea that you work hard too at whatever you do.

There are probably many more reasons, but these are my intial thoughts.

I think people learn from an early age to put labels on everything and they like to lump similar things together, most kids will remember the Sesame Street game, 1 of these things is not like the others for example. So it is only normal for people to want to put a label on somebody they just met by finding out what they do for work because most people define themselves by what they do and by DO I mean work. This gives a whole pile of information about a person with just a few words because what we do often is an indication of how we think, what our income levels are, are we intellectually biased or more physically driven, are we extroverted or introverted, etc. etc. These are just superficial guesstimates because I have known structural engineers who are highly artistic and creative and artists who are very concerned with science and structure in their work or accountants who are extremely extroverted, etc.
When people ask me what I do for a living I now answer them in a way that is truthful but which suits me best based upon my superficial sense of what kind of person they are based upon looks, dress, handshake and how they present themselves. I might just say that I am early retired, or that I am a master builder, or a real estate developer, or a carpenter, or a writer, or a microbiologist, or a politician - all of the above are true but what I tell someone will depend upon who and what I take them for, what I might possibly want from them and just how I am feeling at the moment because I know that they will modify their opinion of me based upon which answer I give them.

Since most of our hours of the day are spent working, I find it fascinating not just what they do, by why that chose that career path. If it's part-time or if they have a few part-time jobs. Do they live for the weekends? Are they downtrodden because of their job? Do they bring their work home with them? Do they have a work-life balance?
I usually ask later and see if I can learn something new from them, different perspective on how they work, even if it's in an industry unrelated.

Forget that. What would you say if a guy asks you how much money you've got in your savings account on a third date?!

It's called small talk. Would you rather me asj you about the weather?

Tells many things, if she's working vs. solely taking care of kids, the type of work can give a clue as to intelligence, advanced degree etc., if she has time to date (some jobs are time intensive) and of course the normal small talk to see if you may have some interest, topic or industry and the people that go with them in common.

So work is something we do for a good portion of our lives. It's the start of a story. If I meet someone that is really smart and she is a waitress, that's interesting to me. Is money not important? Is she in school? Maybe she is a lawyer, do you work for civil rights, Chase ambulances? And then why? I think the why is more important.
Also, I have a curious mind, so I might know something about her job and we can discuss, but also might be able to learn something. The job we pick and why tells an interesting story.

Curiosity. Trying to find common ground, something to talk about, or just learning more about the woman.

I breathe, eat , drink & be merry for a living. No not that kind of MARRY. =0}

I ask because I'm curious about how a person spends their day. Work is such a huge part of our lives, and asking where, or for whom, they work allows a peek into that slice if time. It also might provide fodder for additional questions, if it's an interesting or unusual career/job.

On a date, maybe to learn her education or other things about her personality. One's job reveals much.

Not on a date, it's small talk or may branch to other more interesting topics.

What you do for a living is probably how you spend the majority of time compared to any other activity. It's an easy thing to talk about. If they do something different than me it's easy to ask a follow up question and let them talk about what they do and make them important. If They do something I do or have done we can relate.

I think just to have something to talk about

Artists are flaky? LOL I resemble that.

I think is almost basic to know what. the person you are trying to meet, does for a leaving.. I am not talking about any random person .. but someone you are interested in, and you want to get to know him better.

To determine if she can support you in the manner you're accustomed to.

Just an ice breaker really, not intrusive but shows an interest. I don't think it's any deeper than that.

Although if I met a woman in a wet suit playing a banjo I would ask 'What the fuck do you do for a living?'

Personally it is because I am not great at small talk. I can't think of many other questions I can ask which have an answer worthy of discussion (ie suitable small talk topics) that are less personal.

What question would you ask someone you knew nothing about? Alternative topic suggestions might be quite useful.

The occupation itself may not define the person, but it may indicate the amount of ambition, may show their interests (if they are passionate about the work), and if they'll have time for a guy. If she works a ton or has irregular hours beyond reason, then tjatay not work out so well.

I don't normally ask about work until it comes up in regular conversation. I guess I just don't care that much? I don't feel as if my work defines who I am.
I'd much rather get her talking about something she is passionate about. That makes for a more interesting and informative conversation in my opinion. If that happens to be her job, she'll bring it up long before I will.

Because I have social anxiety and can't think of anything else to say?

I ask EVERYONE what they do for a living. It's just a means of starting conversation.