The Pew Research Center found a majority opposed to government restrictions on online activity in 22 of 24 countries surveyed.
Support was especially high among younger people and in countries with a high percentage of people using the Internet.
Eighty-nine per cent of those surveyed in Venezuela said they supported an unfettered Internet, as did at least 80 per cent in Lebanon, Chile, Egypt, Argentina and Brazil.
The numbers were high in Mexico (79 per cent), South Africa (77 per cent), Bolivia (76 per cent), Malaysia and the Philippines (both at 73 per cent) and Nigeria (72 per cent).
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"It is less common in nations with lower penetration rates, like Indonesia and Uganda," where 55 and 49 per cent, respectively, said they oppose government censorship.
The report comes days after the US government announced it was giving up its key role in charge of the Internet's technical operations, handing over those functions to "the global multistakeholder community."
While US officials said they would work to maintain a free and open Internet, critics of the decision said the move opens the door to other countries to impose new controls on online activity.
Among younger people in the 18-29 age bracket, a strong majority supported an open Internet in every country except in Pakistan, Pew said.
The results from Russia contrasted with those of the rest of the survey, with a relatively low percentage of 63 per cent saying they oppose censorship even though Russia has among the highest levels of Internet use.
The well-educated were more likely to support an open Internet in many countries. In Tunisia, for example, 73 per cent of college graduates said it is important to have Internet access without government censorship, compared with 56 per cent of the overall population.
The margin of error ranged from 3.5 percentage points in Venezuela to 7.7 points in Turkey, with most of the national surveys between four and five percentage points.