Altmetric - Alternative to citation-based metrics. Gives a score for individual articles based on the quantity and quality of attention received, such as tweets and readers in Mendeley and CiteULike (example).
Scopus - Provides citation counts from publications in Scopus but alternative metrics are also included using PlumX Metrics (Plum Analytics) when available.
Web of Science - Provides citation counts from publications in Web of Knowledge databases (highly cited articles are included in Essential Science Indicators). Also provides usage counts from the last 180 days or since 2013. The counts are record exports (to EndNote, etc) and clicks to full text.
Google Scholar - Provides citation counts from items in Google Scholar and links to Web of Science citations for those with access to the database. Watch this 2-minute video on Google Scholar "Cited by" option.
Dimensions - Includes publication citations, linked clinical trials and patents, as well as supporting grants.