There are many articles about how social networks can, or have, change(d) society. Google it! Expect many more in the near future, following the Arab Spring. By any account this involves at least eleven arabic nations.
The protests have shared techniques of civil resistance in sustained campaigns involving strikes, demonstrations, marches and rallies, as well as the use of social media, such as Facebook, Twitter, and YouTube, to organize, communicate, and raise awareness in the face of state attempts at repression and Internet censorship.[src]
25 January 2011: The "Day of Revolt", nationwide protests against the government of Egyptian President Hosni Mubarak began. Tens of thousands of protestors gathered in Cairo, with thousands more in cities throughout Egypt. The protests were generally non-violent, but there were reports of some casualties among both civilians and police.
26 January 2011: "Shutting down The Internet": After several Facebook groups were created and so-called tweets (from Twitter) facilitated mass demonstrations, the Egyptian government decided to shut down Internet access for most of the Egyptian people. This was done to impede protestors' communication.
27 January 2011: Mobile operators suspended SMS and MMS services as ordered by Egyptian authorities. Access to the Internet (Domain Name Service) in the entire country shut down.
Shortly after the Egyptian Internet-shutdown, engineers at Google, Twitter, and SayNow, a voice-messaging startup company acquired by Google in January, announced the "Speak To Tweet" service. Google stated in its official blog that the goal of the service was to assist Egyptian protesters in staying connected during the Internet shutdown. Users could phone in a tweet by leaving a voicemail and use the Twitter hashtag #egypt. These tweets could be accessed without an Internet connection by dialing the same designated phone numbers. Those with Internet access could listen to the tweets by visiting twitter.com/speak2tweet.
Internet service providers such as the French Data Network (FDN) provided free (zero-cost) dial-up access to Egyptians with landline (analog) international telephone access. FDN provided the service as a matter of principle, to "contribute to the freedom of expression of the Egyptian people and allow them to keep a connection with the rest of the world."
28 January 2011: The "Friday of Rage" protests began. Just after midnight, the Egyptian authorities ordered most Communication and Internet services to be shut down in an attempt to disrupt the protests. (As a result, approximately 93% of all Egyptian networks were unreachable by late afternoon.)
1 February 2011: Mubarak made a televised address offering several concessions. He pledged he would not run for another term in elections planned for September, and pledged political reforms. He stated he would stay in office to oversee a peaceful transition.
2 February 2011: Connectivity re-established by the four main Egyptian service providers.
9 February 2011: The heavy filtering that occurred at the height of the revolution had ended and bloggers and online activists who had been arrested were released.
11 February 2011: At 6:00 p.m. local time, Suleiman announced Mubarak's resignation and that the Supreme Council of Egyptian Armed Forces would assume leadership of the country.
2 March 2011: The constitutional referendum has been tentatively scheduled for 19 March 2011.
3 March 2011: A day before large protests against him were planned, Ahmed Shafik stepped down as PM and was replaced by Essam Sharaf.
19 March 2011: The constitutional referendum was held and passed by 77.27%
I left out descriptions of the violence and many protests, but for a complete regime change, it was relatively quick and non-violent. Of course, things aren't settled in Egypt yet (July 2011), with some claiming the change amounted to a (fairly) bloodless military coup. Those involved in the Libyan civil war have not been so lucky.
Did social media play a role? See "Internet role in Egypt's protests" by Anne Alexander at BBC News ("everywhere you look there are mobile phones") and "Exactly What Role Did Social Media Play in the Egyptian Revolution?" by Simon Mainwaring at Fast Company.
"[T]his model of activism an upgrade. But it is simply a form of organizing which favors the weak-tie connections that give us access to information over the strong-tie connections that help us persevere in the face of danger. It shifts our energies from organizations that promote strategic and disciplined activity and toward those which promote resilience and adaptability. It makes it easier for activists to express themselves, and harder for that expression to have any impact. The instruments of social media are well suited to making the existing social order more efficient." according to "Small Change: Why the revolution will not be tweeted" by Malcolm Gladwell at The New Yorker.
Despite the opinions in the last article linked above, Twitter (and other social media) is affecting society today. Did it affect the outcome of the recent (2016) US Presidential election?