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I believe Orkut was Google's first attempt at social networking several years ago. It didn't take off here, but it got popular elsewhere, like South America.
LiveJournal was/is an early blogging network that began around 2000. Early last decade, it was one of the most popular "social" sites. To help LJ's performance, LJ's creator, Brad Fitzpatrick, also created memcached, which still gets implemented by many Web services today.
Stack Overflow is popular among geeks. It's a good source for answers to tech questions. For me, the site appears often in Google search results.
I've been following Quora for a few years. Some early Facebook employees created Quora. It began as a Q&A site for anything. Besides Q&A, it now includes other functions, such as blogging. You can follow users, questions, and topics. Quora could be perceived as being somewhat complicated or hard to understand how it works, but I like it okay. It requires a user to invest a little time checking it out.
Examples of Quora topics:
Stack Overflow and Quora are considered to be "modern" or different takes on forums.
GitHub is mainly used by computer geeks, but it could be used by anyone who wants to maintain version control on writing projects.
O’Reilly media is doing something I haven’t seen before: using github as a repository for a book. Github is a famous code repository, and I have seen it extended to include government data. But this sees like a new way to use it. Expect more non-traditional uses of github.
I visit Hacker News about every day, usually more than one time per day. Y Combinator maintains the Hacker News forum. Y Combinator funds/seeds/founds startups, including Reddit, Scribd, Disqus, Dropbox, Heroku, AirBnb, and Hipmunk. Unofficial Y Combinator Company List.
Justin Timberlake is now one of the owners of Myspace. In the fall of 2012, a new Myspace was unveiled.
Blasts from the past that are not on the list that SensorG posted:
Digg was quite popular approx five years ago, but it imploded due to bad business and design decisions.
Friendster was a social network from about 10 years ago. February 2013 article titled An Autopsy of a Dead Social Network.
I remember Xanga being a popular blogging or social site early last decade.
Facebook launched in February 2004, but it did not open up to everyone until September 2006. So contrary to what many may think today, Web communities or sociallizing on the Web did exist prior to September 2006.
Some may remember Web communities, such as Tripod and GeoCities from the mid-1990s.
The World Wide Web was invented or began in 1989 or 1990. But Internet communities or discussion areas, such as Usenet and bulletin board systems like The Well predate the Web. I think Internet access providers, such as AOL, Prodigy, and CompuServe provided their own online communities back in the 1980s.
Classic read: The Epic Saga of The Well
Today, I enjoy reading two new blogging networks that began in the past year: