ImpactStory is a free tool that allows researchers to build their own profiles and is not attached to any institution. Find out more at https://profiles.impactstory.org/
Altmetric.com (not to be confused with altmetrics themselves) is a commercial provider of altmetrics data. Known for their "doughnut" with a score, many Altmetric.com widgets appear on publisher websites and even in library catalogues. Some Altmetric.com data is available for free, like the Altmetric Bookmarklet for Researchers.
The University Library System provides access to the Altmetric Explorer. It is a web-based platform that enables users to search for and report on attention data of scholarly content.