Netflix and other services to be available on holiday
Online service subscriptions, such as Netflix and Sky's Now TV, will be portable across the EU under proposals announced on Wednesday.
The European Commission also described its plan to overhaul copyright laws, which it said would make it easier to legally buy and use content.
Supporters said the proposals were an opportunity for creative industries.
But some industry bodies attacked them, saying they lacked detail and would cause harm.
Under the first set of proposals, which will need to be approved by the European Parliament before they can be implemented, online subscriptions to services would become portable within the EU.
"People who legally buy content - films, books, football matches, TV series - must be able to carry it with them anywhere they go in Europe," said Andrus Ansip, the commission's vice-president for the digital single market.
The commission said that allowing cross-border portability would mean "enabling consumers to use their home online subscription while they stay temporarily abroad".
It said it expected the regulations to be approved next year and implemented in 2017, "the same year as the end of roaming charges in the EU".
The commission also announced plans - to be turned into more concrete legislative proposals within the next six months - to allow providers to sell content across the EU under a single set of copyright rules, rather than having to draw up various contracts to adhere to national laws.
It later clarified that the BBC's iPlayer would be exempt from the rules because it does not verify a user's country of residence.
"This said, the BBC has announced that it is willing to allow its users to access the iPlayer when they are outside the UK for a limited period," said Nathalie Vandystadt, the European Commission's spokeswoman for the digital single market.
She added that the rules were not aimed at covering all online content services "as it might be too burdensome and expensive for some services to adopt the necessary verification system. For free of charge services, the choice remains open: if they decide to start using verification methods, they can benefit from the rules".
The commission said: "Overall, the commission wants to make sure that Europeans can access a wide legal offer of content, while ensuring that authors and other rights holders are better protected and fairly remunerated.
"The key sectors of education, culture, research and innovation will also benefit from a more modern and European framework."
Mr Ansip said: "When you download a movie or a song, it must play.
"If this is not the case, you should be able to end the contract and get your money back."
He added the proposals would provide a "common set of EU rules instead of a patchwork of national laws".
Alliance for Intellectual Property chairman Richard Mollet called the portable subscription proposals a "huge opportunity for the UK's creative industries, which are globally successful and are enjoyed by hundreds of millions of European consumers every day".
And he said the copyright plans must "enhance the opportunities for creators to sell their content across Europe and help them protect it".
"Alliance members are already working to deliver even better access to content, but we also must ensure that the value of creativity is not reduced, as well as maintaining strong incentives to invest," he added.
But John McVay, the chief executive of Pact, the trade association for the UK's independent media companies, said the commission's portability proposal "falls far short of that goal due to inadequate safeguards to prevent abuse and a lack of clarity in key concepts like the meaning of 'temporary'".
He said: "It is critical that portability is conditional on robust and effective authentication of consumers' country of residence.
"We urge the EU institutions to address these issues as a matter of urgency.
"The commission's proposals to mandate cross-border access to digital content remain a significant concern for producers, distributors and broadcasters of film and TV content in the UK and across the EU."
A BBC representative said: "We are interested in being able to allow UK licence-fee payers to access BBC iPlayer while they are on holiday in the EU, and welcome the European Commission proposing regulation to help make this possible.
"There are complex technical issues to resolve and aspects of the commission's proposal need clarification.
"Being able to offer BBC iPlayer also depends on the UK government implementing legislation to modernise the licence fee to include video on demand as well as linear viewing, something the government has committed to do next year.
"That will mean users of BBC iPlayer could be verified as UK licence-fee payers while they are on holiday in the EU."
A Netflix representative said: "We are committed to providing Netflix members with great programming wherever they are and are studying the EU's proposal."
A Sky representative said: "We will need to consider the plans in detail, but we welcome anything that helps customers get even more value from their subscriptions.
"We look forward to working with the commission to ensure that the proposals are part of a robust framework that supports investment in European content."