Having lived in Italy, my experience is that Italians are pretty obsessed with bottled water. Well really bottled spring water to be exact. At restaurants especially. The exception would be in areas where you can get spring water from the source like a mountain resort. Spain is quite similar although I've only spent months at a time there so I'm less experienced in their views on water.
In the US it varies, but it's still fairly easy to find restaurants that bring a glass of tap water without even asking you. Big city restaurants and upscale restaurants will try to sell you bottled water but asking for tap water is not frowned upon like it would be in Italy.
I haven't spent enough time in Switzerland to comment on that, so maybe you could give more details on your experience there.