MathSciNet® is an electronic publication offering access to a carefully maintained and easily searchable database of reviews, abstracts and bibliographic information for much of the mathematical sciences literature.
Online Tutorial Available Here

Google Scholar is a freely accessible web search engine that indexes the full text of scholarly literature across an array of publishing formats and disciplines. 
Link your search to Wolfgram Library for access to Full Text, from within your Google Scholar search results... find out how below.
Online Tutorial Available Here

Coverage: 1975 - present
ASP provides comprehensive content, including PDF backfiles to 1975 for nearly 140 journals and searchable cited references for more than 1,000 titles. As a leading scholarly database, it provides access to acclaimed full-text journals, magazines, and other valuable resources.
Online Tutorial Available Here

Coverage: varies
Search for peer-reviewed journals, articles, book chapters, and open access content.

SAGE Journal Collection covers multidisciplinary topics and also includes their deep backfile collection.

Coverage: varies
SpringerLink allows searching of articles from hundreds of electronic journals and thousands of electronic books published by Springer and its subsidiaries. Most of the journals and some of the ebooks are available as full-text. 

Note: To search for available full-text content, uncheck the "Include preview only content" box.

Coverage: varies
Taylor and Francis Online is a multi-disciplinary site that offers full-text access to many journals in a variety of subject areas.

Coverage: varies
One of the largest and most authoritative collections of online journals, books, and research resources, covering life, health, social, and physical sciences. All articles are available Full Text.