JournalTOCs is a free service from a non-profit consortium of universities and publishers that provides access to the most recent tables of contents for over 12,000 scholarly journals. Contents lists may be exported to other feed readers (e.g., Feedly, The Old Reader, Newsblur). It also provides links to the fulltext of thousands of articles, with institutional or personal subscriptions.
You can receive new Table of Contents (TOC) for specific journals via email or RSS directly from publishers. TOC alerts will include links to access the specific articles. You will usually have to register for a free account to create email alerts, when those are available.
Note: If you are off-campus and click through to access specific article results in your email or RSS alert, the fulltext articles won't be available unless you are in a proxied browser session. You can do this by adding a proxy prefix to the URL of the page you are on, or by using the NYU proxy bookmarklet link. More information on options for off-campus access is available here.