Were iconic structures intentionally destroyed in 20th century wars?

Two instances come to mind quickly:

1. The bombing of Rotterdam in May, 1940, accompanied with the threat to do the same to Amsterdam and Den Hague in order to coerce a quick Dutch surrender.

2. The destruction of the World Trade Centre Twin Towers, and attempted destruction of the Pentagon, on Sept. 11, 2001.

Given Al Qaida's status in 2001 as a de facto well sponsored arm of the Taliban ruled Afghanistan, I fail to see how anyone can see that particular act as anything but an act of war.

Further, it seems clear that these act, by and of their nature, are deliberate acts of terror, and thus the attempt to split hairs between acts of terror between nations and acts of terror between nationally sponsored organizations pointless.

• the destruction of the Leuven University library/Belgium by German troops in 1914
• the destruction of Couchy Castle/France by German troops in 1917
• the destruction of Warsaw by German troops in 1944
• i am not really sure if bombing raids against centers of civilian population with iconic buildings fit your question or not, but there are quite a lot of examples of this. In Germany e.g. Dresden, Nürnberg etc.
• several towns in East Germany going up in flames right after (or just before?) being captured by the Red Army in 1945, e.g. Neustrelitz, Neubrandenburg, Altenberg (probably not world heritage level, but still valuable). See also the fire in the Friedrichshain Flak Bunker in Berlin in May 1945.

This occurred at least twice in the Vietnam War. I say "at least" because these are the two instances I know of, and there could well be more.

Mỹ Sơn

This complex of temples was built by the Cham in the 15th Century, who (I'm told) were the original inhabitants of Vietnam until who we today consider the ethnic Vietnamese invaded and took over. Cham people still live today in southern Vietnam. These temples were carpet bombed because they were being used by the VC.

When I visited (July 2013), one of these temples was being rebuilt.

Huế Imperial City

This citadel was built in the former capital of the then-Kingdom of Vietnam at the beginning of the 19th Century. Huế was seized during the Tet Offensive, and the Imperial City was a bombing target in the process of reclaiming the city.

The Imperial City was also being rebuilt when I visited, in some cases from the ground up, although much of it still stood and had already been repaired.

The way Vietnam is handling these sites is very interesting to an American; my Vietnamese friend pointed out that, after all, Vietnam won the war. But even so, it's strange to compare these sites to our own war heritage sites.

In the Korean War, the US air force destroyed the Gwanghwamun, which was the gates of the old Korean palace. More info: http://en.wikipedia.org/wiki/Gwanghwamun

Aldo, the Yongmyongsa Temple in pyongyang was destroyed by carpet bombing. Link: http://en.wikipedia.org/wiki/Yongmyongsa

During the Soviet German war (part of the WWII) both sides deliberately destroyed cultural monuments of the other side. The Germans tried to destroy the Uspenskii cathedral, a part of the Kiev Lavra. I only have a Russian language source for this, but there are some photos: http://2000.net.ua/2000/aspekty/istorija/44243 The document mentions names and documents from German archives about this, and cites A. Speer's memoirs.

Soviets deliberately destroyed several German WWI memorials, and even the mausoleum of the famous Napoleonic era general Blucher (Wikipedia article on Blucher).

I am surprised that nobody mentions the example which is going on just now: it is in the news. The "Caliphate" destroys on purpose the ancient cultural sites in Iraq. Of course most of us do not recognize the "Caliphate" as a state, so perhaps this example does not qualify. But this only shows that the question is not well posed: what is a state?

The Islamic State regularly destroys historical artefacts. Here is one from just last week. Here is another. It is widely suspected that they loot and smuggle a considerable portion of the content of the museums and historical sites that they destroy as well.

I'm reminded of the Baedeker Raids of WW2.

Baron Gustav Braun von Stumm, a spokesman for the German Foreign Office, is reported to have said on 24 April 1942 (following the first attack), "We shall go out and bomb every building in Britain marked with three stars in the Baedeker Guide", a reference to the popular travel guides of that name. Goebbels was furious; keen to brand British attacks as "terror bombing", he was equally keen to designate German efforts as "retaliatory measures". Stumm's off-the-cuff remark "effectively admitted the Germans were targetting cultural and historic targets, just what the German leadership did not want to do, and Goebbels took steps to make sure it did not happen again".

Wàn Sōng Temple, China

During the Second Sino-Japanese War, the Imperial Japanese Army and its Chinese puppet auxiliaries set fire to the historic Wàn Sōng Temple, lit. Temple of (Ten) Thousand Pines. The temple was the largest of its kind on Mt. Pán in Ji County, near the city of Tientsin, a famous scenic area. The temple was ancient and once home to the famed Tang dynasty general Li Jing.

When war broke out, Japan quickly swept through much of the region, taking the urban centres without really control the country. Remnant Chinese forces, both regular and irregular, retreated into the mountain to conduct guerrila warfare. In response Imperial Japan instituted a scorched earth policy. As part of the resulting counter-insurgency operations, many of the historic buildings on Mt. Pán were destroyed.

^{(The temple today, rebuilt in 1985.)}

The overt justification for the destruction is contained in the policy that led to it; namely, to suppress guerrilla activity.

The Monastery of Monte Cassino. Which was made worse by the facts that:

• even for the attacker, there were no actual reasons for it, as the Germans were (this time) civilized and did not use the monastery as part of their defenses.

• it worsened the situation of the attacker. Once bombed, there was no cultural reason to declare the ruins "safe ground", and so the Germans did occupy it. And, as Germans knew from Stalingrad, ruined buildings did provide a lot of good defensive positions.

In September 1914, during the first World War the famous French Reims Cathedral was hit and heavily damaged by German shell fire. Reims Cathedral is a national monument of France, not only because of its long history and architectural beauty, but also because the French kings were crowned there.

As far as I know, the German troops undoubtedly aimed for the cathedral and did not hit it by accident. What remained uncertain is why the cathedral was attacked. While the French side in WW I claimed that the cathedral was attacked because it was a national monument, the German side in WW I argued that it was attacked because of military reasons.

More information: Thomas W. Gaehtgens: Bombing the Cathedral of Reims

Edit in reply to @user5001's comment that my answer missed a reference that the cathedral was bombed deliberately:

It is not easy to find hard evidence that the cathedral was bombed deliberately. Stahlgewitter.com has two German reports from the 22nd September 1914. That's 3 days after the bombing took place and after Germany was accused to destroy the cathedral in an act of vandalism. In my opinion these to articles are an attempt to white-wash the incident.

The second article, an official bulletin of the German Army says:

• We [the German HQ] gave order to spare the cathedral as long as the enemy doesn't use it.
• On the 20th of September the French raised the white flag over the cathedral, but put a field artillery observer on the tower.
• It was necessary to remove the observer. We fired shrapnel shells at the cathedral, but not heavy artillery.
• We stopped firing at the cathedral afterwards.
• We blame the French that they misused this venerable building despite showing the white flag.

The German HQ doesn't say anything about the bombing on September 19th - they start a day later. But even in this white-washed bulletin they confirm that they aimed for the cathedral.

In my opinion that's enough evidence to prove that the German Army bombed the cathedral deliberately. What remains unclear is whether they did it because of military reasons or in the intention to destroy a national monument.