Recently in Istanbul, massive public demonstrations were sparked by plans for building development in a favourite city park - and popular opinion holds that a set of new tower blocks has ruined a view of the ancient Hagia Sophia, which had remained unchanged for centuries.

But many greet sensational additions to their city's skyline with delight. So what is it with spectacular new buildings in places normally known for more traditional architecture? Are they sources of pride, or reasons for riot? Are they scandalous scars on the face of a city, or do we sometimes forget that the buildings we now lump together as "old" were sometimes built centuries apart, and that individuals among them, when new, may have met with just such outrage?

From Lego blocks to the Carlsberg logo, from Bang & Olufsen electronic equipment to Arne Jacobsen chairs, Danish design has long been making an impact. Architecture, too. The Sydney Opera House, surely one of the most recognisable buildings in the world, is by a Danish architect. And Copenhagen, famed for the charm of its brightly coloured waterside buildings, has a cluster of stunning contemporary additions to its cityscape.

On a sunny day, the polished granite cladding of the Royal Danish Library, known as the "Black Diamond", reflects ripples in the harbour waters alongside, like a giant vertical sheet of oil. Its hard-edged, trapezoid shape stands out sharply against a historic backdrop.

Although the Black Diamond created some mutters when it was built at the turn of this century, it's now a firm city favourite, as a nickname often indicates. East of the city centre, the black-and-white-flecked Bella Sky Comwell hotel, with its tilting towers and zany angles, makes an even stronger impact. "Danish architecture is of high quality, but often understated," says Copenhagen resident Carsten Magnus Haandbæk.

"It rarely challenges the viewer, but the Black Diamond and Bella Cloud are real exceptions."

This spring, 3XN (the architects behind Bella Cloud) added another eye-catcher to the Copenhagen skyline - a glinting metallic, whorl-shaped aquarium, Den Blå Planet, The Blue Planet. "It's amazing, like a spaceship just landed by the sea," says one impressed visitor waiting in the queue to get in.

Development around former dockland has brought a dash of bravura architecture to Amsterdam, a Dutch city better known for its low-rise brick façades and dinky decorative gables. First off the mark was Renzo Piano's copper-clad NEMO building (a science museum), thrusting into the eastern docklands like a giant ocean liner. The newest arrival is the EYE, an aerodynamic zigzag that is the home to Amsterdam's world-renowned Film Museum. Locals have welcomed both with delight - NEMO is already something of a city icon, and the EYE has become a hip hangout.

Indeed, the way that people use a building can often be a more eloquent statement of how they have taken it to heart than any grand pronouncements of aesthetic value. "What strikes me most about the JKK centre is the amazing cafe and common areas, where people from all walks of life share the cultural melting-pot ambience," says NGO worker Ian Forber-Pratt, about the Jawahar Kala Kendra arts centre in the Indian city of Jaipur.

A place of age-old fortresses, maharajah's palaces and tumultuous bazaars, Jaipur is dubbed the Pink City for the soft hue of its Old Town walls. Rather than pursuing an exotic Western style, Charles Correa - the man acclaimed as "India's greatest architect" - works from a deep empathy with indigenous techniques and forms. He has placed the nine parts of the JKK centre around a calming central square, a design based on ancient Hindu astrological principles, and underlying the original layout of Jaipur itself.

But, in another context, Correa absorbs different influences, and comes up with an entirely contrasting style. His brand-new Ismaili Centre in Toronto, Canada, soars upwards in a glass-and-steel pyramid, in the midst of city parkland.

"I like the design," says local student James Worthington. "It's bold, but isn't causing as big a scandal as Daniel Libeskind's giant crystal-like extension to the Royal Ontario Museum did a few years back. The centre fits right in with the modern cityscape of Toronto and will for years to come."

Tension between local and indigenous styles is often a sore point. The beautiful Indonesian island of Bali has seen a wave of new villa buildings. Some sport the materials and features of traditional joglos, pitched-roof houses. But many flourish streamlined, one-step-ahead, more Western takes on Balinese courtyard living - such as Ali Reda's Villa Tangga, with its Aztec-temple rake of stairs, or trademark lopsided abstract-shaped roofs from architects Gianni Francione and Mauro Garavoglia.

"Bali is one of those rare places where you'll find a traditional Javanese joglo on top of a cliff, or a striking glass structure in the middle of the jungle, and yet the Balinese aesthetic and spirit is felt throughout the space," says long-time resident Hana Makrim.

Not everyone agrees. "I think most of the new stuff is totally over-the-top and hideous," says regular visitor Asmeen Khan, though she does like the villas that blend in and use local elements.

So, monstrous carbuncles, or stunning new style? For many, the jury is still out.