The outspoken general secretary of the Rail, Maritime and Transport (RMT) union died in a London hospital after reportedly suffering an aneurysm followed by the heart attack early yesterday morning.
Paramedics had worked to save his life for an hour. His older brother Richard said he was a "loveable little rogue" adding that the family were still trying to establish how he died.
Left-winger Mr Crow was often vilified by right leaning commentators for his rhetoric, exotic foreign holidays and the fact he lived in a council house despite earning £145,000 a year.
But London Mayor Boris Johnson described him as a "fighter and a man of character". The Conservative, who clashed with him over last month's London Tube strike: "Whatever our political differences - and there were many - this is tragic news. Bob fought tirelessly for his beliefs and his members. It's a sad day."
Ex-London Mayor Ken Livingstone said: "He fought hard for his members. The only working-class people who still have well-paid jobs in London are his members."
He said Mr Crow was "broadly right on most key issues" and that if more people had fought for the conditions of the working classes "this country would be a much better place".
Manuel Cortes, leader of the TSSA rail union said: "Bob Crow was admired by his members and feared by employers, which is exactly how he liked it. It was a privilege to fight alongside him because he never gave an inch."
Labour leader Ed Miliband said: "Bob Crow was a major figure in the labour movement and was loved and deeply respected by his members. I didn't always agree with him politically but I always respected his tireless commitment to fighting for the men and women in his union."
The Prime Minister's spokesman said David Cameron express-ed his "sincere condolences" to Mr Crow's family and friends.
Liberal Democrat leader and Deputy Prime Minister Nick Clegg said Mr Crow had been a "fighter and a force".
John Cridland, director-general of the CBI, said: "Bob Crow was a doughty and committed advocate for his members."
The Essex-born Millwall football fan campaigned against the Iraq conflict, Trident, the Royal Mail privatisation and international struggles. Floral tributes were left at the RMT's London headquarters, which were closed out of respect. It said his death had left a "massive gap".
Mr Crow succeeded the late Scots-born Jimmy Knapp, more than a decade ago. On Monday, Mr Crow had said he was worth his salary. Of recent photographs of him sunbathing in Brazil before a strike, he added: "What do you want me to do? Sit under a tree and read Karl Marx every day?"