Delegates at the party conference in Brighton also voted without any opposition to renationalise the Royal Mail, should it be sold off before the general election.
In two separate motions put before conference, the unions called on Labour leader Ed Miliband to renationalise the railways if he wins in 2015 and ensure the Royal Mail is returned to public ownership.
But a senior Labour source dismissed the idea. He said renationalisation of privately-owned services was not the party's policy.
There has been tension at the conference during the week between the Labour leadership and the unions following the row over party funding.
On Monday, Len McCluskey - general secretary of Unite - told the conference that "no one is pushing us out of our party".
"We are here to influence our party, to urge it to stand up and demonstrate it is on our side," he said.
And yesterday, party treasurer and union official Diana Holland warned Mr Miliband the financial stability of Labour could be jeopardised if he went ahead with his controversial reforms.
Today, the unions tabled an emergency motion calling on Labour to renationalise the railways. A similiar motion was passed at the conference in 2004 but it did not make it into the general election manifesto in 2005.
While policy motions passed at the Liberal Democrat conference form the basis of the party's manifesto under its rules, any passed at the Labour conference do not commit the leadership to making them party policy.
But today's votes - and the overwhelming way in which they were passed - show the strength of union feeling on the possibility of renationalising private services such as the railways, energy companies and even previously publicly-owned services such as British Telecom.
The votes could also lend support to Mr Miliband's critics, who say he is undermined by the strength of the unions in the wider party.
Labour sources have been keen to stress the insignificance of the votes.
A senior source said: "Renationalisation is not our policy. Conference is entitled to its view. We are going to do the right thing. We are not going to spend money we do not have."
The comment came after Tosh McDonald, vice president of the train drivers' union Aslef, said it was "a nonsense" that most of the railways remain in private ownership, claiming that higher fares should not subsidise investment in the network.
In a speech to support a motion for Mr Miliband to make the renationalisation of the railways party policy, Mr McDonald said East Coast Mainline, which is publicly owned, made £800 million for the Treasury, while only 1.3% of its income came from the taxpayer.
By comparison, he said, the Virgin-run West Coast Mainline took 13% of its income from the Government.
Mr McDonald said: "When we say the arguments to sell East Coast off again are led by ideology, it is. Ideology is not all wrong. Our ideology is the right one and we shouldn't be afraid to talk about the ideology of public ownership.
"Whether it's the railways, the power companies, the water companies, the gas or electric power companies, or telecommunications or the post service, it doesn't matter - they are natural monopolies, natural monopolies that should be in public ownership and those that make a profit should subsidise those that don't make a profit.
"Isn't it a nonsense when we are told by public power companies that they have to put their bills up to us, when railways put their fares up to us so that we can pay for investment, so that they can make more profit? It's a nonsense."
Meanwhile, the Communication Workers' Union (CWU) led the calls to keep the Royal Mail in public hands. It insisted that Labour, if elected in 2015, could pay off any re-purchase price within a few years by using Royal Mail's expected profits.
Billy Hayes, CWU general secretary, said the next Labour government should renationalise the service if the coalition "gets away with selling it".
He told delegates: "If it falls into the hands of private companies there will be an increase in prices for all the companies, all the small businesses and consumers who use this network.
"Keeping our postal service will make a major contribution and avoid further rises in a cost of living crisis.
"The coalition Government is not just selling Royal Mail, it's offering bribes to investors. Already before a single share has been sold they are offering a £400 million dividend - £200 million in 2014, £200 million in 2015.
"The debate about cost and priorities, a Labour government could pay off any repurchase price within a few years of the profit from Royal Mail. We can demonstrate that and we will to any independent inquiry."
He was supported by Labour backbench MP Katy Clark, who claimed it would be a "disaster" for postal services should privatisation go-ahead.
Manuel Cortes, general secretary of the rail workers' union the TSSA, welcomed today's vote on the railways.
He said: "This will be a real vote winner on the doorstep and will help Ed on his way to Downing Street.
"Passengers have seen fares more than double to the highest in Europe since John Major's disastrous sell off 20 years ago.
"(Former transport secretary) Philip Hammond was right, they are now a rich man's toy beyond the means of many families.
"This will put a stop to that rip off system which has benefited the few, Sir Richard Branson and Brian Souter, rather than millions of ordinary fare passengers who still face yearly increases above the inflation rate for at least the next five years."
Mr Hayes also welcomed today's other vote on the Royal Mail.
He said: "I strongly welcome the decision of Labour conference to both continue opposition to the sale and to renationalise Royal Mail if it has been sold by the current government.
"A postal worker will deliver to every address in the UK today, six days a week, every week of the year. Royal Mail is part of the fabric of a One Nation society."
He added: "Labour's conference decision should raise a warning flag for potential investors. Poll after poll has shown public opposition to the sale, and with the company making substantial profits, there is no economic argument for the sale.
"There is still time for this Government to listen to the public, consumers and the businesses and user groups who have campaigned under the Save Our Royal Mail banner and drop this politically dogma driven sale."