The MLA International Bibliography with Full Text contains the full text of more than 1,000 journals including 60 important linguistics-related journals, such as: Applied Linguistics, The Canadian Journal of Linguistics, The Canadian Journal of Applied Linguistics, Cognitive Linguistics, International Journal of Applied Linguistics, etc.
JSTOR (Journal Storage), is a large, full-text archive of back issues of journals across a wide range of academic subjects. It contains back issues of many journals to the first issue. To find the most recent research on a topic, use one of the other databases on this page.
A multi-disciplinary database that will have some information on almost any topic. It indexes journals such as Applied Psycholinguistics, Journal of Pragmatics, Lingua, etc. An excellent place to find a couple of articles on a topic, if you're in a hurry. For more in-depth research, use one of the specialized databases in this list.
A comprehensive index, no login required, that is similar to the citation indexes of Web of Science. Each citation provides a list of its references and a citation count plus a list of citing documents. Limited full text, though there is an open access filter on the left. For more full text and formatted citations, take titles found in Dimensions, log into Google Scholar from the library home page, and search for Dimensions titles there.