The urban cores are very old, but many of them are surprisingly small, with the bulk of the city dating to the past 100-150 years. Copenhagen's old center, for example, was less than 10km across (confined within city walls until the 1850s), so nearly the entire city was laid out according to 19th- and 20th-century urban plans (the 20th-century one was http://en.wikipedia.org/wiki/Finger_Plan).

The city where it's architecturally most visible is probably Barcelona, where you can see the medieval core's winding streets, and then a massive expanse of centrally planned regular squares outside of that: http://en.wikipedia.org/wiki/File:Eixample_aire.jpg