Someone made some helpful stickers for the London underground to help people understand that there should be no talking or eye contact of any kind. 
Personally I usually enjoy it.
Perfect.
How I react varies a lot, but I usually don’t cut anyone off.
excuse me. would you repeat that again. my mind wandered off and i wasn’t paying attention.
It depends on context. If I’m just standing under a street light watching traffic go by & minding my own business and someone just rolls up to me I suspect they want something from me and I wish they would leave. If I’m waiting in line for something I might start or allow myself to be drawn into inane banter about the weather, the event we’re queued up for, or whatever else just to pass some time. If it gets weird I grab my nose & squeeze it til it bleeds (easy for me–takes a second) and excuse myself. I sometimes feign being Arabic, which is totally disarming because I don’t look Arabic.
If it gets weird, you up the ante? 
Well…yeah?
I would LOVE to be a fly on the wall for those conversations!
It really depends on the situation. Most of the time I nod and smile and say very little (particularly if the person is a weirdo which more often than not they are). I guess this is my way of being polite yet not encouraging the converstaion. If I am in a taxi and I feel like engaging then perhaps I will ask questions or make more fulsome comments in return.
Unless it’s someone trying to sell me something (or save my soul, which I would argue is the same thing) I will humor them for a few minutes.
I’m fairly patient. I generally like to talk to people, so usually I don’t mind. If I am really not in the mood, I might humor them for a few minutes and then tell them I need to concentrate on something.
I’m generally receptive to people who want to chat. I tend to talk a lot, but (I hope!) I know when to shut up when someone doesn’t seem to want to talk.
This is the perfect time for this anecdote, too. 
The other day I was in the tire shop, waiting while they rotated my tires. I don’t remember how it started, but two gentlemen and I were talking about stuff, and it led to the point of “this country is going to hell in a handbasket” kind of talk. Oh yeah - it had to do with the AC being out because someone had stolen the AC units for the copper.
So this woman who hadn’t uttered a word before said she knew why. and we proceeded to have a conversation about good and evil. She went on and on and preached and proseletyzed, and I tried to steer the conversation away from the Bible, and one of the guys buried his head in his phone and the other guy’s car was ready (woo-hoo for him!)
Eventually I got pretty uncomfortable, and racked my brain on how to get her to shut up. Finally I said, “In all due respect, I’m full. Do you understand?” She took it pretty well, and shut up, and I went back to my book. After about five minutes her car was ready, and we said goodbye, nice talking to you, blah blah blah.
I said to the remaining guy, “Well, that got out of hand!” He said, “You handled that perfectly politely.”
I’m not there for some stranger’s amusement. Sorry, find another victim.
I try to be very, very polite to everyone. You never know who you’ll bump into later in a situation where you want them to be nice to you. Do unto others and all that.
However, there are very polite ways of saying, “Gee, that sounds really interesting, but I’m in the middle of something.”
I’m pretty patient. A person who’s initiating that kind of conversation is probably someone who feels lonely, and if I can make them feel better without any major inconvenience to me, then I’ve earned my gold star for the day.
If I want to discourage them, I usually start by giving very short and noncommittal answers. Lots of “Oh. I see. Mmmhmm. Yeah.” kinds of answers. Most people will take the hint and find someone else to talk to after a little while of that.
If that doesn’t do the trick, my fallback is usually my PDA (now smartphone). I’ve had one since the days of the Handspring Visor when the batteries weren’t even built in, and in a public setting when someone might talk to me, I’m almost always reading or playing a game when they start the conversation anyway. So I can say something like “I have something really important that I need to review before my next client appointment” or something like that, and carry on reading.
If that doesn’t work, I go find a bathroom. If I go into a stall and close the door, I’ve never had anyone try to continue a conversation there.
It’s very annoying when ppl wanna talk and I don’t. I try to ignore them and become ignorant.
(ignorantly) Why are you ppl talking?
As I’ve aged, my appearance has taken on a certain authoritative demeanor. Due to this, no stranger just randomly wants to talk to me (I’m kinda intimidating). Therefore, if someone does approach me to talk, they are are not doing it randomly - they want something. Yay! To me they are a meat version of a telemarketer call - “So sorry, not interested”.
Since I’m a real chatty cathy with strangers in public, I’m fairly tolerant of those who engage me on the rare days when I’m feeling more closed off.
Seems only fair.
Depends. If I’m reading something, not very. It’s usually pretty obvious. I have a book or a Kindle in a book-style cover; these are not easily missed. If I’m listening to a podcast, I have earbuds in and a plausible excuse to blithely ignore people.
If someone is in line at the store or standing on the corner with me waiting to cross, and makes a generic “to anyone listening” observation about something inane like the weather or how the bus schedule always lies, I’m usually willing to be “anyone”. Circumstances usually mean we won’t be together very long. I also try to smile and say thank you to people who deliver compliments en passant and aren’t trying to corner me into a longer conversation.
If someone seems to have zeroed in on ME for some reason, I get very wary and try not to talk at all. I don’t consider train platforms to be an appropriate venue for hitting on me (or trying to convert me to a different religion/political party), and as a rule I don’t encourage people when they do it.
All of this depends on my mood, and often where I’m going as well. I once had a lengthy conversation with an older gent on the train who took one look at me and asked if I was on my way to the symphony, as he couldn’t possibly think of anywhere else I might be going in that dress. I was, and since he was a traveler and Boston is notoriously confusing, I ended up walking him to Symphony Hall.
Worse than unwanted talking is unwanted touching … much much worse.
I was sitting on a bus when a stranger sat down beside me and began to talk to me. He keep tapping my arm to emphasize some point he was making.
As soon as he did it once, I told him in no uncertain terms that I did not like that and I asked him to stop that and never do it again.
He did it once more and I told him again in an even more forceful way not to do that.
He then stopped and did not do it again.
But the question is just how far should you be willing to object to something like this and just what should you be prepared to do?
He only ever tapped me on the arm. He never took it any further than that. But I hated it and I really felt like smacking him.
It really is situational for me. On the CTA, I ignore everyone. Someone trying to talk to me is either grifting or crazy. Yes, even if they stand in front of me and say, “m’am. M’am?” Nope. Can’t hear you. Just asking directions, fine, but that only works if the person is just blurting out the question. If they are trying to get my attention first, I’ll keep ignoring them unless it’s obvious they’re a tourist/suburbanite. I will interrupt to help if I hear other people trying to figure out where they’re going, but that’s it.
I’ve had delightful conversations with cab drivers, small store clerks, people waiting in line, people in waiting rooms, whatever. But someone I know before they speak that I don’t want to talk to them? La La La, can’t hear you.