The demonstrations come in the wake of a March 29 court order in Chennai asking 15 Indian Internet providers to block access to file-sharing websites such as Pirate Bay.
In New Delhi, a group of about 50 people gathered near the historic Jantar Mantar, which has also been the site of protest by Anna Hazare and Baba Ramdev.
"Without Internet, people cannot be liberated. Internet penetration is already low in the country and it (government) is putting a cap on this as well," said one of the activists.
Holding banners, the members of the group raised slogans like, "Raise your voice, save your voice."
"With censorship of Internet, the government is taking us back wards," added another participant.
Many others are supporting the campaign online through various forums like blogs and social networking websites.
There were reports of low turnout at various locations. A supporter, however, tweeted: "Astonished that people focusing on "low turnout" for #opindia. Really? One month ago no one knew them. Today, several cities have protests."
Earlier in the day, Anonymous attacked the websites of CERT-In and Government of India, though later in the day, the portals became operational.
"www.cert-in.org.in and www.india.gov.in are our targets... india.gov.in was down till afternoon. We will be hitting it again after today's protests," the Group said.