Higher densities change the character of neighbourhoods, but given growing populations you need to build somewhere. That means that someplace is going to get changed. NYC is quite densely populated - over ten thousand per square km in 2000 and rising. What I'm talking about here is whether a strip of old industrial area lying between a six lane road plus rail tracks and a very pretty old low to mid rise area should be developed as high rises or not. The proposed development is also right next to a commuter rail station and the highest concentration of subway lines after downtown and midtown Manhattan (both primarily office districts), making it ideal for high density living. The nice neighbourhood will remain intact, its skyline will change and there will be more people in the area. My neighbourhood which lies on the other side of that big road and is also beautiful will see that skyline from the other side. We'll be fine.  

As for ruining the character of a city - I don't know about that. Areas like the Upper West Side have their own character even though the main streets tend to be built up quite high

_Maybe if Americans were not so insistent on living in single-family homes, rather than in apartments... _

Well yes, but again, I'm in NYC, so you're preaching to the choir...