There are a number of impact factors based on traditional publishing and citation.
The Journal Impact Factor is a measure of the citation rates related to journals. It's formed from the citation rates of individual articles, but is not directly applicable to individual articles.
The Eigenfactor and Article Influence scores are attempts to provide a more meaningful measurement of journal and article impacts. Both can be seen immediately within the Journal Reports above, and after 6 months openly at Eigenfactor.org.
The h-index (Hirsch-index) is a basic measurement of citation rate of individual authors. The h is the number of papers by the author (or group of authors) that have been cited at least h number of times. So an author with an h-index of 10 has 10 papers that have been cited at least 10 times each. Obviously, this measure is biased towards highly productive and long career researchers. The index can also be biased by the source of the citation counts. Web of Knowledge and Google Scholar both provide h-indices for individual authors, but because they each monitor different sets of journals and citations, they tend to retrieve different citation counts, and therefore produce different h-indices. Because different disciplines publish and cite at different rates, the h-index is also affected by discipline, and is sometimes shown as a ratio of the individual's h-index related to the average h-index within their field.
Google Scholar also provides the i10index, which is simply the count of papers cited at least 10 times. Both the h-index and the i10-index can be modified by dates (citations within the last 10 years, for instance) which somewhat moderates the career length bias.
These days, citation is not the only way for a publication to gain notice and have influence. Tracking more public mentions of work can be especially useful in fields with a strong public service component and when applying for grants and other funding from funders concerned with public impact and public good.
Our EBSCO databases (CINAHL, Medline, PsycInfo, etc.) are rolling out PlumX Metrics, which tracks usage within the databases, including downloads, online reading, emailing, etc. It's available currently in CINAHL, and may be rolling out in other databases soon.
ImpactStory tracks public mentions of publications, such as news, Wikipedia, F1000, Twitter, and Facebook. Using the researcher's ORCHID ID and the publication's DOI, ImpactStory can track a sort of public awareness of someone's work. ImpactStory also analyzes measures of accessibility, such as openness, readability, and geographical interest. (See an example.)
Since ImpactStory uses DOIs to track works, it can be very useful to use a DOI granting repository to host data sets, slide presentations, white papers, reports, and other works not published in DOI-using journals.