From their websites many journals offer the opportunity to subscribe to a free e-mail-based table of contents alerting service for new issues. On a more comprehensive level you can also let PubMed send you regular e-mails with new articles on selected subjects (via your individual MyNCBI account). A comparable service is offered by our EDS Discovery Service (create your own account via the “Sign In” link at the top of the EDS screen).
And if it’s browsing in self-selected journals you are looking for, you should really try BrowZine, the comprehensive table of contents alerting service for thousands of ITM subscribed-to and open access journals, with direct linking to full-text content. ITM patrons can effortlessly construct their own personal “bookshelf” consisting of up to 64 self-selected journals they wish to browse regularly for new content.