But today, UNESCO's World Heritage Sites - the creme de la creme of monuments and architecture - still face these same threats, along with some new ones, such as heavy-duty tourism and air pollution.
No one is too surprised that important sites - such as the Great Pyramids of Giza - are now under threat.
But even in wealthy countries, such as Britain, some of our most precious ancient structures are at risk. Last month, eight of the great stones in the 4,000-year-old circle at Avebury, Wiltshire, were defaced by graffiti, which inspired copycat attacks in Somerset and Wiltshire.
The attacks are one new worry for curators, whose chief concern until now has been coping with the pressure of growing numbers of visitors and the surrounding 20th-century blight. Sir Jocelyn Stevens, chairman of English Heritage, yesterday said two of Britain's 14 World Heritage Sites, the Tower of London and the Houses of Parliament, were "absolutely wrecked by traffic".
Another cause for shame is the nearby buildings and structures, which seem ugly and inappropriate. Britain's worst example is the Sixties visitor centre next to Stonehenge, a brutal concrete construction which funnels visitors into an underpass leading them beneath the A344 to the stones.
Yet at least the monuments themselves are intact, and more popular than ever. England's ten World Heritage Sites attract over13 million visitors a year, half of them from overseas, with huge gains to the national and local economies.
The problems facing Britain's sites pale in comparison with those in Third World countries.
The huge temple complex of Angkor Wat in Cambodia suffered grievously from almost 20 years of war. It was peppered with bullets and shell fragments and surrounded by mine fields. Then the jungle invaded, with tree roots prising apart its stones. Carved masonry was stolen. Even so, says Ann Le Maistre of UNESCO in Paris, there are grounds for hope since the 200sq km, 1,200-year-old monument, was inscribed on the list of World Heritage Sites in 1992. Visitors to the monument are increasing, giving the Cambodian government an incentive to conserve it. Legislation to preserve monuments has been enacted and a national organisation set up to look after it.
In the next century it will be commonplace for tourists arriving at a great site to be offered two very different experiences.
The first is a quick round of an interpretive centre, where the history and function of the place would be explained, aided by virtual reality techniques.
The second experience will be to actually enter the site itself. The visitor doing this will be expected to commit much more time - half or all of a day - possibly pay more and pre-book.
Taj Mahal: Its marble is under threat of erosion from acid rain caused by nearby industry burning high-sulphur coal, major roads, and thousands of tiny petrol- burning electricity generators which start up during the area's routine power cuts. Unesco, the Asian Development Bank and the Indian government have collaborated on a $100m (pounds 65m) scheme to tackle air pollution, but the government has stalled its implementation.
Dubrovnik: This treasure of the Adriatic in Croatia was heavily shelled by Serb forces during the conflict between Croatia and Serbia during the early 1990s.
However, since then the historic town has undergone extensive repair and restoration.
Tower of London: Marred by a busy five-lane road running just outside it, a disappointingly empty moat and ugly buildings and structures next door. Improvement plans, including filling the moat, are under way but English Heritage's hopes for the road to go into a tunnel - which would cost many tens of millions of pounds - seem very unlikely to be realised.
Stonehenge: Arguably Britain's most important monument, spoilt by heavy traffic on two A roads next to it and an ugly, inadequate visitors' centre. English Heritage has ambitious, expensive plans which involve gradually closing off the roads, building a new visitors' centre more than one mile away and allowing more dedicated tourists to walk among the stones again - something they have not been able to do for many years