Academic Search Premier (EBSCO) is a solid starting place for most research topics. The database indexes thousands of scholarly journals. To limit your search to academic journals, click the Scholarly (Peer Reviewed) Box before you enter your search terms.
JSTOR is a journal archive with thousands of full-text articles. However, because of its archival nature, there will generally be a three to five year window in the currency of the articles. Be sure to explore the Discipline(s) and/or Title(s) to limit your search.