I live in Seattle and we have our share of weird, bizarre, and usual architecture. We have the Seattle Experience Music Program (EMP)- people love it or hate it.  But it’s certainly not the only piece of architecture that defines a city and puts it on the map.  Here are a few other notably weird entries.
Seattle EMP

By Rebecca Kennison (Own work), CC-BY-SA-3.0
Bucharest bizarre
Romania:  Headquarters of the Bucharest Architects’ Association
By Bogdan (Photo by Bogdan) [GFDL or CC-BY-SA-3.0]

Sheffield, The Hubs - geograph.org.uk - 793551
England:  Sheffield Hallam University‘s Student’s Union

Photo by:  Chris Downer [CC-BY-SA-2.0]

City Hall, London, SE1 - geograph.org.uk - 846811
England: City Hall, London

Phillip Perry [CC-BY-SA-2.0]