Well, let me put it this way; Do you think manners are still relevant?
Are people less manner-able today than in years past?
Do we confuse manners and common sense? Or are they one and the same?
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Ah, forgot another question; Do you think parents alone should be responsible for teaching children about manners?
In the US, I feel that manners--often intertwined with friendliness--depends on your location. Where I grew up in Northern California, people in general weren't very nice and often rude and people would look at you funny if you held the door open for someone. Even smiling at a stranger was often seen as a threatening gesture. Where I now live in Washington state, I feel that the majority of people are a lot friendlier, kinder, and are more polite than any large population of people I've encountered. Even in the big cities here, people are still more polite than people I've encountered all over California.
I feel as if manners and common sense should be considered as one in the same. I feel that if you're just going out of your way if you're trying to be rude to someone else. How hard is it to say "please" or "thank you" in any situation?
Where I live there are no manners at all. Kids are constantly disrespectful to their parents and teachers. However, with the parent issue I feel that home environments are different everywhere, and especially with mine.
Common courtesy also doesn't exist anymore. I can be going to the gym and 80% of the time the older generations will hold the door open for me, while only about 5% of the younger generations hold doors. I'm 18 and hold the door open for anybody, which should say something about the younger kids.
I would say that manners do depend on location. Here in southernmost Texas, it's literally the standard to be rude to one another. People usually don't give two shits about anyone other than themselves - very everyone for themselves type of deal. And to a point it is actually quite understandable; we are in close proximity to the U.S./Mexican border and there's a lot of weird shit that goes down here. Simply giving someone a wrong look whether you meant it or not, is enough to get you killed, anywhere. The environment is tense and most of us, if not all of us, have nobody else to count on but ourselves.
I've traveled to other parts of the U.S. where people are definitely much friendlier, namely the Pacific Northwest (Oregon, Washington State, etc).
As far as manners/common sense is concerned... they could go hand in hand, but in my experience, no. Greeting a stranger in Oregon/Washington State is different than greeting a stranger here. Both of them are acts of good manners/common courtesy but one of them could possibly get you killed if you're not careful! Of course, in southernmost Texas, I do make exceptions (such as holding a door open for a disabled elderly woman), but not without caution as criminals can be quite creative in baiting people into being mugged/raped/killed/etc.

I agree with the notion that it depends on location.
However, I attend a university of students (mostly from my state) who overall seem to be very friendly and have decent manners, and it is pretty lame on those rare occasions when you're right behind someone leaving a building and they can hear you following, but they let the door slam in your face. I couldn't imagine not taking that half-second to turn my head and see if there's someone behind me.
Also, common sense and manners are two different things to me. I go by their dictionary definitions.
Yes. Do you see people shanking each other over nothing? We've eliminated slavery in some parts of the world and people have more rights. Hell, the fact that there's ANY rights at all means some manners have progressed...
We've still got a long way to go, but things have definitely improved.
I believe that we haven't placed a high value on manners in recent years. Parents are responsible, most definitely. Common sense does have some part in manners but not 100%.

I think manners depend on where on your location is. Common manners should be taught by parents, but other manners should either be common sense or the child learns by themselves. I live south of central Texas, people here aren't perfect with their manners, but most of them at least have some manners. I have noticed however that more adults than kids will hold the door open for somebody, though.
Of course manners are still relevant. Perhaps, it has changed but there will always be manners. It's not always the same but somehow I think it changes at times when needed to be while others ignore it. Manners can be different for each cultural heritage too. But sometimes we also get influenced by other cultures (see Japan's history?)
Do you think parents alone should be responsible for teaching children about manners? Initially, but if the child goes to school already I do believe the teaching staff/admin should be partially responsible as well. I don't know about other schools but I think it's pretty common to teach good manners and right conduct in primary school, yes? If I'm not mistaken, some people also get help from professional people for these sort of things (anger management, anyone?).