Note: Rankings vary all over the place; As of May, 2012 Pinterest is ranked 14 at alexa, 5 at Quantcast, 3 at Mashable.
See also: Top 15 Most Popular Social Networking Sites (eBizMBA.com) - Unique global monthly visitors

January 2015
eBiz|MBA - Top 15 Most Popular Social Networking Sites (eBizMBA.com)
Alexa - Analytics for the Web - Rank in the US amongst all sites.
Top 10 overall: Google, Facebook, YouTube, Amazon, Yahoo, Wikipedia, Twitter, Ebay, Linkedin, Reddit.

Site	alexa	eBiz	Description
Facebook	2	1	A social utility that connects people, to keep up with friends, upload photos, share links and videos.
Twitter	8	2	Social networking and microblogging service utilising instant messaging, SMS (Short Message Service - Texting) or a web interface.
Linkedin	9	3	A networking tool to find connections to recommended job candidates, industry experts and business partners. Allows registered users to maintain a list of contact details of people they know and trust in business.
Reddit	10		User-generated news, entertainment and social networking posts and links. Votes promote stories to the front page
Imgur	11		Image hosting service, curated in real time by a dedicated community through commenting, voting and sharing.
Pinterest	26	4	An online pinboard: a place where you can post collections of things you love, and a[euro]oefollowa[euro]\0x9D collections created by other people.
Google +	28	5	An information network where people can share and follow interests rather than a purely social site like Facebook.
wordpress.com	32		Blogs managed by the developers of the WordPress.org software
Tumblr	34	6	A blog hosting platform offering customizable templates, bookmarklets, photos, mobile apps, and social network integration.
Instagram	36	7	An online photo-sharing and social networking service that enables its users to take pictures, apply digital filters to them, and share them.
Stumbleupon	51		allow users to discover and rate Web pages, photos, and videos that are personalized to their tastes and interests
Flickr	91	9	Picture galleries available with chat, groups, and photo ratings.
VK	??	8	largest Russian social networking service in Europe. VK allows users to message contacts publicly or privately, create groups, public pages and events, share and tag images, audio and video, and play browser-based games..
Blogger	94		A weblog publishing tool.
BuzzFeed	100		Find the the movies, music, and products that are on the rise and worth your time.
mashable	112		News weblog about social networking web sites and Social Media
wordpress.org	123		Software for creating a website or blog.
Vimeo	130		Community for storing and distributing video content. Includes advanced privacy options, interaction for members with common interests, group projects, and tools for creating widgets.
Yelp	131		Members share their favorite recommendations - everything from the latest restaurants and shops, to the best hair salons and spas, to doctors and yoga instructors.
MeetUp	138	11	Helps groups of people with shared interests plan events and facilitates off line group meetings in various localities around the world.
DeviantART	155		Gallery of digital works submitted by members.
LiveJournal	158		A media platform that willfully blurs the lines between journaling and social networking.
Ask.fm	179	13	Users can ask other users questions, with the option of anonymity
PhotoBucket	258		Provides image hosting for auctions, live journals, blogs, message boards, personal websites and online photo albums. Reliable, fast and very simple to use.
Vine	279	10	Allows users to record and edit five- to six-second-long looping video clips, and to "revine", or share others' posts with followers.
match	284		Online dating
Digg	432		A news aggregator with an editorially driven front page, aiming to select stories specifically for the Internet audience such as science, trending political issues, and viral Internet issues
Tagged	680	12	A social networking site that allows members to browse the profiles of other members, play games, and share tags and virtual gifts.
CafeMom	822		A community where moms can ask questions, give advice and share personal experiences, covering issues from fashion to work.
FourSquare	931		Members note their locations with a mobile phone and can find out where friends are.
Ning	1158		A social networking platform to explore and express interests, discover new passions, and meet new people around shared pursuits.
MySpace	1233		Social Networking Site. Overtaken by Facebook.
MeetMe!	1524	14	Meet new people and chat online
Delicious	2725		Allow users to discover and rate Web pages, photos, and videos that are personalized to their tastes and interests
Classmates.com	4022	15	help users find classmates and colleagues from kindergarten, primary school, high school, college, workplaces
Squidoo	8716		Allows anyone to post a lens about a topic that they have expertise in.

site	Alexa rank		Visitors/mo.		Soc. Netw. Guide * Users (M)	Description
	US	Global	eBiz| MBA global	Quant- cast U.S.
Facebook	2	2	750	143	1,010	A social utility that connects people, to keep up with friends, upload photos, share links and videos.
Twitter	10	10	250	94	500	Social networking and microblogging service utilising instant messaging, SMS or a web interface.
Linkedin	12	14	110	46	187	A networking tool to find connections to recommended job candidates, industry experts and business partners. Allows registered users to maintain a list of contact details of people they know and trust in business.
Google +			65		200	An information network where people can share and follow interests rather than a purely social site like Facebook.
Blogger	13	12	75	48		A weblog publishing tool.
Pinterest	14	35	85	44	20	An online pinboard: a place where you can post collections of things you love, and "follow" collections created by other people.
Tumblr	18	32	60	52	120	A blog hosting platform offering customizable templates, bookmarklets, photos, mobile apps, and social network integration.
wordpress.com	27	22		53		Blogs managed by the developers of the WordPress.org software
Instagram	43	73		3	32	An online photo-sharing and social networking service that enables its users to take pictures, apply digital filters to them, and share them.
Yelp	45	204	40	19		Members share their favorite recommendations - everything from the latest restaurants and shops, to the best hair salons and spas, to doctors and yoga instructors.
Flickr	60	66	90	12		Picture galleries available with chat, groups, and photo ratings.
Reddit	61	128	16	27		User-generated news links. Votes promote stories to the front page.
DeviantART	84	131	25	11	24	Gallery of digital works submitted by members.
match	91	376		18		Online dating
PhotoBucket	103	180	75	18		Provides image hosting for auctions, live journals, blogs, message boards, personal websites and online photo albums. Reliable, fast and very simple to use.
Vimeo2	111	138	17	16		Community for storing and distributing video content. Includes advanced privacy options, interaction for members with common interests, group projects, and tools for creating widgets.
wordpress.org	121	105		2		A semantic personal publishing (blogging) platform with a focus on aesthetics, web standards, and usability.
BuzzFeed	125	408	14	15		Find the the movies, music, and products that are on the rise and worth your time.
MySpace	149	232	70	10		Social Networking Site. Overtaken by Facebook.
MeetUp	156	528	8	3		Helps groups of people with shared interests plan events and facilitates off line group meetings in various localities around the world.
Squidoo	176	224			14	Allows anyone to post a lens about a topic that they have expertise in.
Tagged	200	280	20	4	100	A social networking site that allows members to browse the profiles of other members, play games, and share tags and virtual gifts.
Ning	319	383	12	3		A social networking platform to explore and express interests, discover new passions, and meet new people around shared pursuits.
CafeMom	340	1,513	12	16	8	A community where moms can ask questions, give advice and share personal experiences, covering issues from fashion to work.
mashable	257	320		4		News weblog about social networking web sites and Social Media
FourSquare	722	622		0.1	20	Members note their locations with a mobile phone and can find out where friends are.
LiveJournal		134	21	5		A media platform that willfully blurs the lines between journaling and social networking.
Bebo		4,231	2		117	High school and college social network (like MySpace and Facebook), makes it easy for high school and college students to stay in touch with their friends, find long lost friends, and meet new people.

2. Vimeo is a video sharing site like YouTube. Vimeo fits into a much more niche audience, centered on good filmmaking and inspiring videos. Vimeo filters out the commercial videos, gaming videos and all non-user generated content. - See more at SparklOftMedia.com.
YouTube is in the top 4 of all web sites, but is generally not counted as Social Media.

See also The Users Of Social Media - MediaBistro.com
Quantcast - Top Ranking U.S. Websites Unique US visitors
Top 15 Most Popular Social Networking Sites (eBizMBA.com) - Unique global monthly visitors
Social Networking: A Beginners Guide, Winter 2012/2013 - Magazine at B&N
Alexa - Top Sites in United States
Social Networking Websites Review 2013 - TopTenREVIEWS.com

Notes:

Determining number of users and visitors is difficult.
 - Many users sign up and never use the service or only use it infrequently.
   Some sites are fads for a year or so and then popularity drops.
   e.g. Many MySpace users moved to Facebook but still have MySpace accounts
 - Users may set up multiple accounts for themselves
 - Users may access their accounts from multiple computers, mobile devices or locations
   Quantcast has an algorithm to try and correct for this.
    See Cookie Corrected Audience Data - White Paper