It's perhaps tangential to your question, but there are a number of international agreements in place to just that: obviously mark and (hopefully) preserve objects and locations of cultural heritage in times of war. (Please note: I am by no means a scholar of international law.)

The first major piece of international law meant to protect cultural landmarks in war was Section II, Article 27 of the Hague Convention of 1899, which mandates that "...all necessary steps should be taken to spare as far as possible edifices devoted to religion, art, science, and charity, hospitals, and places where the sick and wounded are collected, provided they are not used at the same time for military purposes. The besieged should indicate these buildings or places by some particular and visible signs, which should previously be notified to the assailants." However, there's no provisions for what shape those "particular and visible signs" should take, nor on their size.

Section IX, Article 5 of the Hague Convention of 1907 was more or less an addendum to that of the 1899 Convention regarding the protection of cultural artifacts, this time dealing with naval bombardment, making it the responsibility of the commander of the attacking force to spare those same locations specified in the 1899 Convention. Notably, however, the 1907 Convention makes it the responsibility of the inhabitants to mark such locations in a specific manner: "It is the duty of the inhabitants to indicate such monuments, edifices, or places by visible signs, which shall consist of large, stiff rectangular panels divided diagonally into two coloured triangular portions, the upper portion black, the lower portion white."

Similarly, the proposed Hague Rules of Air Warfare, written in 1923 but never adopted, extended similar protection from aerial attack in articles 24 and 25.

In 1935, the United States and nine other countries in the Americas signed the Roerich Pact. Nicholas Roerich was a Russian artist and thinker, an early champion of the defense of cultural artifacts in wartime, and his ultimate goal was to create a symbol and a body of international law that was for cultural property what the Red Cross was for medicine. The Pact was the first realization of that goal, and though its legal reach is fairly limited as only ten countries ratified it the Roerich Pact was greatly influential in its ideas, in particular after World War II. Roerich's proposed symbol was the Banner of Peace, and while it is still a legal protective sign in the ten countries which ratified the Roerich Pact it has since been superseded.

Roerich's idea was far more fully realized in 1954, when the Hague Convention for the Protection of Cultural Property in the Event of Armed Conflict was signed, and currently 128 states are party to the treaty. In addition to protections for fixed properties such as buildings and monuments, this convention specifically protects moveable cultural properties--books, paintings, sculptures, etc--as a reaction to the Nazis' theft of artworks in the Second World War. Also, a special protective sign was specified to mark protected cultural properties. The International Committee of the Blue Shield was established in 1996 as a direct analog of the International Committee of the Red Cross for the protection of cultural property, taking its name from that symbol. The 1954 First Protocol was extended in 1999 by a Second Protocol, adding categories for special protection, creating a fund to protect cultural property, and providing for punishments for those who violate the protections of the treaty.

See also: Wikipedia's page on protective signs.

I just finished Thomas Madden's book about Venice and he talks a little about this in WW2.

Basically there was a concerted effort on the allies part to not bomb Venice at all. They could afford to do this of course because there was very little strategic value in Venice.

There was however a single bombing campaign to destroy Axis shipping that was going through Venice. It was done with a great amount of planning and precision and they were able to take out the targets without harming the city. The citizens of Venice watched the raid from their rooftops.

The book also includes the quote "Provided you weren't Jewish, Venice was the safest place in Europe to be during WW2"

I can't speak to the entire span of human history, but on a more modern note, Colin Powell discussed this very subject in his autobiography. (I'm away from home at the moment and don't have the book with me, so this will be less specific than I'd like.) During the run up to the Gulf War in spring/summer 1990, he and other American military commanders were discussing potential bombing targets in Baghdad. Anti-aircraft installations, military bases, airfields, and offices, and communications/transportation infrastructure were obvious targets for crippling the Iraqi military's ability to fight. However, they also drew up a list of statues and monuments that they felt had propaganda value to the Hussein regime and could demoralize the Iraqis if lost. The list was given to the military's legal branch for approval, and the legal eagles refused to sign off on bombing anything in the latter category because they could be considered culturally-significant artifacts and had no strategic importance. So yes, even ugly statues of Saddam Hussein were to be left unmolested by the Air Force, and anyone caught violating or overlooking this could potentially be handled a dishonorable discharge or jail time. Someone dryly remarked that the lawyers were running the war.

General Powell and his British counterpart were also concerned about Saddam Hussein's potentially unleashing chemical or biological attacks on coalition soldiers, and not without reason. While the American military had trained and equipped its soldiers for this possibility, it was still one that Powell was terribly worried about, and he wasn't sure how best to prevent it. He sat down one day and drafted a potential letter to be sent to Hussein in the event that war was formally declared, and warned that, if any chemical or biological attacks were detected, the U.S. military would destroy the dams on the Tigris and Euphrates rivers in retaliation. The only possible result would be the catastrophic flooding of Baghdad and enormous human suffering. The letter was never sent -- Powell admitted that it was an empty threat and that no one in the U.S. military or government would ever sign off on it -- but I don't remember offhand if he or anyone else came up with alternative ways to convince Hussein to stick to conventional weapons.

So the answer with respect to American rules of engagement in the early 1990s is that, yes, cultural icons enjoyed a special protection, as did houses of worship, hospitals, schools, markets, residential neighborhoods, and critical infrastructure like dams and sewer systems. Basically, anything that was likely to exercise disproportionate impact on the civilian population was off-limits.

P.J. O'Rourke also had an amusing tidbit in Give War a Chance, which contains an account of his time as an ABC radio reporter during the Gulf War. Someone from the U.S. military was fielding questions at a press conference about potential bombing targets in Baghdad. (And by the way, if you want a funny look at how dumb many of these questions really were, Saturday Night Live ran a skit on Gulf War briefings on February 9th, 1991 that was within shouting distance of reality. Transcript here if you can't see the video.)

A reporter got indignant and said something along the lines of, "Aren't we going to leave the Iraqis any government offices at all?" A British wire reporter sitting nearby said, "We'll leave them the Department of Tourism. See the ruins."

Edit: Fixed a word.

One of the many depressing aspects of the wars during the break up of Yugoslavia was the specific targeting if cultural icons.

Although the military aim of most battles was to establish control over territory and the people within, in areas where a specific structure held a specific significance to one side, especially in mixed areas, the destruction of the icon became a military objective.

The most famous example is the bridge at Mostar, which had been built by the Ottomans in the 15th century. This was destroyed by Croat paramilitaries, as they saw the land as Croat and Catholic, not Bosnian and Muslim. This also had a significant morale effect on the besieged Bosnians, but also lost the Croats in Hercegovina a lot of international goodwill.

Earlier, Dubrovnik's Old Town (rather than the more strategic harbour) was the target of heavy shelling from the Yugoslav army as Croatia broke away from the Federation.

The statue of Ivo Andric in Sarajevo (the Nobel Prize winning author from Višegrad in Bosnia, who identified as Serb) was beheaded by Bosniaks as a gesture against Bosnian Serbs.

To summarise, in answer to the original question: no, and sometimes the cultural significance can make it a target.

This is not a direct answer to the question, but here's a good paper I found explaining the game theoretic reasons why an international reciprocal agreement can work.

http://scholarship.law.cornell.edu/cgi/viewcontent.cgi?article=1509&context=cilj

International law, in this sense, exists in a state of nature, because there is no overarching legal authority with compulsory jurisdiction to enforce agreements. Inevitably, reciprocity has become an important ele- ment in relations between sovereign nations and in the body of existing international law. This paper begins with setting up a taxonomy of social interactions, in a game-theoretic framework,4 to examine the role of reciprocity in the functioning of international law and whether reciprocity is, in effect, a meta-rule for the law of nations.

As you might imagine, the payoff matrix can change causing such agreements to fail.