Likewise interesting hearing about the US. Just like there are differences between American cities, there of course are differences between European ones as well, although general patterns are visible in both cases.
One thing I think would be a bit surprising to an American visitor who haven't seen much of the major European cities is the absence of a skyline. Few European cities display a downtown concentration of skyscrapers. Cities like Copenhagen and Stockholm have more or less banned "real" skyscrapers, while some other European cities have allowed a few.
I guess Frankfurt-am-Main, Germany, is the closest thing to an American city in this respect. Warsaw, Poland have some skyscrapers too, but it's not exactly New York or Chicago.
Paris and London have some skyscrapers but they are scattered around.
Here in Scandinavia, I'd say we have ONE(!) skyscraper:
Turning Torso in Malmö.
I like it a lot. It's really unique in the way it actually is a turning, twisting, high rise structure. Furthermore, these construction principles will be used when erecting
"World Trade Center Tower 1"/"Freedom Tower" in NYC.
http://en.wikipedia.org/wiki/Turning_Torso
http://en.wikipedia.org/wiki/Freedom_tower