We’re talking about strangers, right? Not males we happen to know and see while out and about.
C. I noticed you looking at me, and yeah, you’re cute too. (I’m a redhead, that draws attention even if I’m not a knockout)
I don’t know how I feel about the “approach me” part of A so it doesn’t exactly mean that, and I’m not a people person, so unless it’s a little kid being adorable, it’s never B.
I never smile and make eye contact with strangers. This may be why I’m single 
Post removed as I just realised this was specifically for single women. Sorry!
So I can file it away for future reference, what flavor do you like?
I tried
It’s usually B, occasionally C, and if it’s A, you’ll know, because I won’t wait for you to approach me if I’m interested.
Is it really that hard to tell the difference? It’s not like all eye contact and all smiles are created equal.
Not single or looking right now, but:
Most days, if I make eye-contact with someone accidentally or otherwise, I automatically smile. It’s mostly a “Oh look, another human being! I have noticed your presence! Congratulations on that whole being alive thing, and I am now going to hold the door for you/get out of your way/whatever action seems appropriate at the time” and then I look away and move on.
Smiling that indicates the OP’s option A is generally accompanied by longer eye contact and a wide grin rather than a quick smile.
B or C, with C covering a lot of possible reasons. Everything from “Check, please!” to “That’s a cute dog” to “I am trying not to laugh at your horrible comb-over” to “I’m not in a good mood but am trying to look cheerful so people don’t ask me what’s wrong or worse still pull that ‘You’d be so pretty if you smiled!’ crap on me.”
It wouldn’t ever be A with me.
Too funny! 
For me, it’s being friendly to a stranger. If I thought someone was cute, I wouldn’t be able to look at them!
Heh. I try.
I pretty much smile at anyone upon whom I find my eyes resting. If you smile back, and I continue to look, then there’s more to it.
For me, it’s something like A. I don’t make eye contact with strangers because I don’t want men to feel like I’m giving them an invitation to approach me. If I do it, I must be flirting.
Assuming I was single, A or B (since I’m not, it’s B).
There’s a difference though - if I was flirting, I’d look away then look back again to see if the cute guy was doing the same
If I’m just being friendly, I don’t look back, I just continue doing whatever I was doing.
the most common reason in everyday life is B. I live alone so I try to make an effort to actively engage/acknowledge the people around me when I;m out of the house (holding doors, saying please and thank you and excuse me - smiling and nodding to I pass - the smile to acknowledge cute kid or pet antics etc.)
But If a particular someone catches my eye, the A is certainly a possibility.
In general though, If I’ve made eye contact and acknowledged someone I wouldn’t be upset if that person came up to me and began a conversation. I can’t promise I’d say yes if they asked me out, but I don’t normally mind chatting/passing the time with stangers in a public place. If I want to be left alone, I won’t make eye contact to begin with.
Almost always B for me, too. I also work in a job that requires friendly contact with strangers, so I find myself leaving the hotel, heading to the grocery store, and still smiling and making eye contact with everyone in the store. It’s a hard habit to switch on and off at will. I also find myself doing this in more “social” situations, like stopping in for Happy Hour somewhere, so I always try to go places where I’m going to know at least several people already. If I’m sitting at the bar with my best male friend, most guys aren’t going to misinterpret my smile of greeting as a flirtatious smile. If I’m sitting alone at the bar, the smile is apt to be seen as more “inviting,” I guess.
I suppose possibly B, if I’m feeling social, and I’ll be polite to and smile in the general direction of servers and cashiers as a matter of course. The odds are against eye contact happening at all, and it’s almost certainly an accident if it does - I find it quite painful to look people in the eyes, so I’m usually looking at their nose or forehead.
ETA: I don’t generally find people randomly attractive - I need to be talking to them first, and even then it will probably take awhile. That doesn’t mean I’ll turn you down if you ask me out, though - I’ll probably say yes and see how it goes, so give it a shot.
I’m a Southerner. I smile at people because there are people walking by or because I am working and it is my job to smile. I really freaking hate it when men get all gross at me because I up and smiled at them.
I had to really be careful in France, as a smile with eye contact was obviously a clear come-on there.
B - just doing the polite and civil thing. Perhaps particualrly if there is some delay in a shop queue or or waiting for a 'bus or something unusual or striking or amusing happens - shared nod of friendship, blah. See, I would assume that he wouldn’t be interested in me anyway. Yeah, Pessimism is me. 
B for me as well. I do it with everyone. In truth if I DO find someone attractive, I tend to avoid eye contact. But that’s just a personal issue.
I finally got around to reading the men’s thread. Guys, buck up! Our answers might mostly be B, but there’s no reason to jump to a negative C all the time! I’m betting the lot of you are better looking than you seem to be giving yourselves credit for.
Shoulda posted this in the Men’s Thread. 
But even if we are making up reasons that a girl wouldn’t want to smile at us, if all your answers are B, it still doesn’t matter.
There has to be at least one attractive male in the Men’s Thread, but look at all your answers. You can’t and won’t look at a guy you find attractive?
We are all fucked up.
EDIT: “All” meaning men and women.