A majority of participants in a global BBC poll believe the internet has brought greater freedom, but more than half of those interviewed also think it is not a safe place to express their opinions.
Many believe that greater freedom goes hand in hand with increased government surveillance, according to the study commissioned for the BBC World Service.
People in countries with a tradition of media freedom are less likely to think their national media free to report truthfully and without bias.
The poll was conducted in 17 countries around the world and is being released as part of Freedom Live, a day of broadcasts on the World Service's 27 language services exploring the idea of freedom and what it means**.
The results show that freedom, never a simple notion, has become ever more complex in the digital age. The internet and social media mean we can communicate more freely than ever. But we are also under more surveillance than ever before from governments and commercial organisations.
The poll found that more than two-thirds (67%) of those questioned agreed that the internet had brought them greater freedom, with only a quarter disagreeing.
Agreement was lowest in Mexico, Germany and China: in the last two countries barely half of those questioned (51%) agreed.
At over 75%, it was highest in Nigeria and Kenya - countries which until recently were bedevilled by poor communications infrastructure, and where mobiles and the internet have had a transformative impact, especially in business - as well as in the UK and Australia.
Nigeria also topped the poll of countries where people feel they are safe to express their opinions online, closely followed by India, Indonesia, Pakistan, Kenya and Peru.
In all those countries, more than half those questioned said they felt safe speaking their mind.
But in general, a majority of people (52%) feel unsafe online.
The fear is greatest in France and South Korea, closely followed by the other European countries in the poll, as well as the US, Canada and Australia.
In China, opinion is nearly evenly divided: 45% said they felt safe saying what they thought, against 51% who said they felt unsafe.
"There is an increasing sense that everything you do online now is being monitored, or at least can be monitored, by either governments or corporations," says Caroline Baylon, a research associate in the international security department of think-tank Chatham House.
"What if, as a result of a political opinion you express online, a government decides to put you on a terrorism watch list? And corporations are also watching what you do.
"There are companies out there whose sole business is to gather data on your online activities, create a profile on you, and then sell that information onwards. What if employers purchase that information? Could something you post prevent you from getting a job?"
She says government actions are partly to blame for this climate of suspicion.
"I think Edward Snowden's revelations of widespread spying by the US National Security Agency, including on its own citizens and close allies, have undercut trust in the actions of many governments," Ms Baylon notes.
"Such large-scale surveillance is no longer the prerogative of authoritarian governments like China."
That no doubt helps to explain another - at first sight surprising - result from the poll.
Respondents were asked whether they felt free from government surveillance online.
More than one in three (36%) said they did not, but the figure was highest in some of the countries which like to think of themselves as bastions of freedom and democracy: In both the US and Germany, more than half those surveyed thought they were not free from government surveillance.
On the other hand, when the pollsters asked the same question in China and Russia, a large majority (76% in China) answered that they did feel free from online surveillance.
Lionel Bellier of the pollsters GlobeScan, who carried out the research, thinks one possible explanation for this apparently counter-intuitive finding may be different levels of internet penetration: Around 80% of American and German households have internet access, but the proportion is less than half that in Russia and China.
"Countries with high internet connectivity feel more exposed to the Snowden era of online surveillance compared to countries with low levels of internet-connected homes," he says.
"In countries with lower connectivity, perceptions of what constitutes government surveillance are felt and lived differently, perhaps with less anxiety.
The pollsters also asked people about the media.
Global news organisations like the BBC like to boast of their freedom from government and other outside influences. In the developed West, media freedom is supposed to be a given.
But according to the survey, only 40% of people around the world believe their own country's media are free to report the news accurately, truthfully and without undue bias, and by no means all of them are in Europe and North America.
The figure is highest in Indonesia, where 73% think their country's media are free.
In the UK, the figure is 45%. In the United States, supposedly the land of the free with a First Amendment guarantee of a free press, it lies at 42%. In Mexico, Russia and Pakistan, the figure is 26%, in France 24%, and in South Korea a paltry 14%.
How free you feel, it seems, is not necessarily a reflection of how free the society you live in is nominally supposed to be.
** The poll results are drawn from a telephone and in-person survey of 17,589 adult citizens across 17 countries conducted by the international polling firm GlobeScan and its national partners on behalf of the BBC World Service between December 2013 and February 2014. The 17 countries were: Australia, Canada, China, France, Germany, India, Indonesia, Kenya, Mexico, Nigeria, Pakistan, Peru, Russia, South Korea, Spain, the United Kingdom and the USA.