Few, however, have lingered in the mind longer than something that happened 95 years ago, in 1919.
The red flag had flown over the square the previous day - Black Friday, January 31 - as strikers fought with police.
The following day, tanks and thousand of troops were sent in to Glasgow to quell what the government believed was a 'Bolshevik rising'.
It has become a landmark event in Scotland's industrial history, and a key part of the militant Red Clydeside legend, the memory of which has lasted to this day.
There had been examples of Glasgow militancy during the First World War - notably the famous Rent Strike of 1915, led by such figures as Mary Barbour, which saw the government cave in, and introduce a Rent Restriction Act.
The Great War ended in 1918, and soldiers began to return home. But by the following year, unemployment was frighteningly high, especially among soldiers.
The government was deeply worried when a strike was called in Glasgow January 1919 in pursuit of a 40-hour week.
As the eminent historian, Tom Devine, wrote in his 1999 book, The Scottish Nation: "A 40-hour strike had been called to support the demand of the STUC that the working week should be cut to help reduce unemployment which was increasing as demobilization accelerated.
"The strikers were trying to prevent the removal of war-time regulation of wages and control of rents."
On January 27, an estimated 40,000 men downed tools in the shipyards and the city's engineering shops. By some estimates, 70,000 workers were out.
On the 29th, workers at the Port Dundas electric power station joined in.
That same day, a deputation from the influential Clyde Workers' Committee went to the City Chambers to ask the Lord Provost to send their message to the government.
On Bloody Friday, January 31, an estimated 60,000 men, women and children crowded into George Square to learn from the Lord Provost the official reply to their request for a 40-hour week.
The red flag flew over them, as it usually did.
However, the government had that morning already made plain its response.
The strikers in the square found a large police presence between them and the chambers.
Some delegates, including Davie Kirkwood, entered the building in order to talk to the Lord Provost. Others, such as Willie Gallagher and Manny Shinwell, spoke to the crowd.
Suddenly, the police laid into the strikers with their batons. Contemporary reports suggested that some strikers had refused to allow tramcars to pass, which prompted the baton-charge.
Confusion reigned for the next hour. Strikers threw stones, and bottles they had liberated from a passing lorry.
The battle spread to Glasgow Green and that night there were sporadic clashes in other parts of the city. Gallagher, Kirkwood, Shinwell and other leaders were all arrested.
Wrote Devine: "The evidence suggests that there was no revolutionary conspiracy, despite the flaunting of the red flag, and that the disorder was sparked by police over-reaction."
But the Scottish Secretary of State at that time told his Cabinet colleagues what had occurred was a 'Bolshevik uprising', added Devine.
The fears of government ministers and middle-class people alike had already been inflamed by the Russian Revolution of October 1917.
The next day, in Devine's words, Glasgow was 'an occupied city'.
That Saturday, some 12,000 troops were stationed at key locations across Glasgow. No fewer than six hulking tanks took up position at the Gallowgate. A barbed-wire cordon was put around the City Chambers.
The message was clear: no radical working-class agitation would be permitted.
The strike fizzled out - but its implications were felt for years afterwards, in terms of both the national political picture and the labour movement.
According to Tom Devine, the episode deepened many Glasgow workers' disillusionment with the political establishment and hastened support for the Labour Party. Some of the strike leaders -Shinwell and Kirkwood - became nationally-known figures.
In 2009, on the 90th anniversary of Bloody Friday, sociologist Dr Seán Damer, writing on the BBC Scotland website, described its legacy.
"It demonstrated that workers could achieve results by rank-and-file mass demonstration and self-organisation," he wrote.
"Ironically, the police riot strengthened the overall working class movement.
"And during these events, engineering unions concluded an agreement for a 47-hour week, which meant that workers now started at 0800 instead of 0600, a very considerable gain.
"The Clydeside agitation had played a vital part in that concession."