Here in the suburbs, I think the fences are common. When I replaced the old wood and chain-link fence back in 2000 in my back yard, I just did it. My south neighbor had some privacy fence bolted to my/his/our dividing fence. I said, “Hey, I’m going to replace this fence. How’s it affect yours?” He told me just to have the fence company not haul it away. When they were done, he put it back up himself, and actually did it nicely with U-bolts and such so as not to screw up my new chain link fence. However, the ugly side is definitely facing me. And since my fence is in the way, I can’t even paint it. Now there’s a new owner – I should see if there’s a code for maintaining the appearance of it facing my side.
Oh, but I didn’t ask my neighbors to contribute at all. If I were in a higher-class neighborhood, I might consider it. In my case, let’s see – I pay half, and the other half among three neighbors – that’s asking them each for $190. It doesn’t seem like much, and all of a sudden I’m disappointed in myself for not having asked! Dang, it’s only $190!! And it would have saved me 50% on my fence!
As for taking care of things, we kind of do this in relation to driveways. My south neighbor actually owns about 3" of “my” front and side lawn along the driveway, and we own about 3" of my north neighbor’s on their side, and so on. But we pretty much just use the driveway as the demarkation point. If I refuse to cut my south neighbor’s grass, it’s my yard that looks like crap! Then of course there’s the point at the ends of the driveways where they flare out. They actually flare out enough that we extend into each others property lines. But since this is the “city” part of our yard (the easement) I guess it doesn’t matter.
Of course the fencing I’m talking about is suburban fencing, you know, where we live like rats (not as ratty as city rats, though) and every house is close to every other house*. In spacious areas – not necessarily rural or country, and not necessarily rich neighborhoods – I would expect fences more akin to what Duckster describes, and fewer (ugly) chain link fences.
*actually for some reason the new modern subdivisions are worse. The houses are huge but the lots tiny; literally separated by nothing but the width of their driveways! And they have ugly chain link fences (as do I).