The Impact Factor is the most widely-recognized method for attempting to gauge a journal's rank/importance. It is particularly well-known in the Sciences and Social Sciences.
The impact factor is based on two figures: the number of citations to a given journal over the previous two years (A) and the number of research articles and review articles published by that journal over the same two-year period (B), so: A/B = Impact Factor
Note that there is a discrepancy between the type of content counted for each factor: A = any type of content (including letters, news items, etc.), but B = research or review articles only, making the Impact Factor not a true average.
Journal Citation Reports allows you to search for a journal by title, browse by journal, or browse for a journal by category. The same journal may appear under several categories, and its impact will vary according to the group.
Here are the results for a search in the Behavioral Sciences category:
You'll see that additional metrics, such as the Eigenfactor and Article Influence scores, are also captured in this display.
From the Journal Citation Reports Help pages:
The Eigenfactor Score calculation is based on the number of times articles from the journal published in the past five years have been cited in the JCR year, but it also considers which journals have contributed these citations so that highly cited journals will influence the network more than lesser cited journals. References from one article in a journal to another article from the same journal are removed, so that Eigenfactor Scores are not influenced by journal self-citation.
Article Influence Score
The Article Influence determines the average influence of a journal's articles over the first five years after publication. It is calculated by dividing a journal’s Eigenfactor Score by the number of articles in the journal, normalized as a fraction of all articles in all publications. This measure is roughly analogous to the 5-Year Journal Impact Factor in that it is a ratio of a journal’s citation influence to the size of the journal’s article contribution over a period of five years.
The mean Article Influence Score is 1.00. A score greater than 1.00 indicates that each article in the journal has above-average influence. A score less than 1.00 indicates that each article in the journal has below-average influence.
From the Thomson Reuters web page:
Informed and careful use of these impact data is essential. Users may be tempted to jump to ill-formed conclusions based on impact factor statistics unless several caveats are considered.
When considering the use of the impact factor (IF), keep these aspects in mind:
Impact factors have often been used in advancement and tenure decision-making. Many recognize that this is a coarse tool for such important decisions, and that a multitude of factors should be taken into account in these deliberations.
Using Impact Factors within a given discipline should only be done with great care, as described above. Using impact factor data to compare journals across disciplines is even more problematic. Here are some of the reasons: