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"Academics use Academia.edu to share their research, monitor deep analytics around the impact of their research, and track the research of academics they follow." Like SSRN, this is a platform for sharing research which also includes analytics.
Some analysis free, most not. Uses Elsevier's Scopus data. Includes social media (Pinterest, FB, Twitter, Google+), reference managers (Mendeley, CiteULike), blogs, mainstream media outlets (e.g., NYT as well as major non-English langauge publications), and more.
Webometrics: Site to track impact across the web. Collects and aggregates data from multiple sources to produce a single impact report. Sources include Facebook, PLoS, SlideShare, Topsy for tweets, mendeley, delicious, citeulike, Scopus, Wikipedia, PubMed and more.
"... everyone should be able to review each other's work, not just the elected few. This is why PaperCritic now offers researchers a way of obtaining and providing feedback for each others work in a fully open and transparent environment." Powered by Mendeley.
PLoS Impact Explorer
"Check which articles are seeing the most buzz from social media sites, newspapers and in online reference managers." Mashes data collected by altmetrics for papers published by PLoS data.
This page lists the metrics supported by Plum. Plum X is a subscription-based product.
[As of November, 2013, this start-up seems to have stopped. Will test again.] "Using readership-based metrics we can estimate impact on the basis of the consumption of scientific content by a population of readers. ReaderMeter adapts two popular impact metrics for authors (the H-Index  and the G-Index ) and redefines them using bookmarks instead of citations as an HR-Index and a GR-Index respectively: hover over the index values for an explanation of their meaning. Analysing readership data can help discover areas of real-time impact that may not be visible to traditional citation-based measurements [3-5]. Readership data is made available via the Mendeley API."
This is a social framework based on crowdsourced annotations of scholars,"designed to keep up with the rapidly evolving disciplinary and interdisciplinary landscape." It applies Google Scholar data to its "social tool to facilitate citation analysis and help evaluate the impact of an author's publications."
"...a web service that collects Article-Level Metrics for scientific articles. Everyone can register via his/her Twitter account and can then add articles from PubMed via the DOI or PubMed ID." This tool "uses freely available sources for the Article-Level Metrics," including Twitter, Mendeley, PubMed Central, CiteULike, Wikipedia and CrossRef.
Social Science Research Network
"composed of a number of specialized research networks in each of the social sciences. Each of SSRN's networks encourages the early distribution of research results by reviewing and distributing submitted abstracts and full text papers from scholars around the world....SSRN's objective is to provide rapid worldwide distribution of research to authors and their readers and to facilitate communication among them at the lowest possible cost." (Depending on what you want to do, this network may include costs.) Site-specific metrics: “top papers,” “top authors,” and “top institutions.”