RePEc offers various tools to keep abreast of latest research developments in economics. Keep in mind that due to the unusually long refereeing and publication process in this field, following what is coming out in journals is often not the best way to keep current. The research frontier is advancing with working papers, and this is why RePEc puts a special focus on those. Note that all resources below are free, as always for RePEc services.
NEP
NEP (New Economics Papers) offers email lists and RSS feeds that disseminate approximately every week the latest online working papers across over 90 fields. Field-relevance is determined by volunteer editors who pick the appropriate papers among all working papers newly listed on RePEc during the previous week. Note that if you think a topic is not appropriately covered, you can volunteer as editor of a new report.
MyIDEAS
MyIDEAS allows you to follow new additions to JEL codes, author profiles, series and journals. This is done through the creation of an account on the IDEAS website. Once logged in, you can add the relevant items while navigating the site.
EconPapers Search
EconPapers allows to limit the search results to documents added recently to RePEc. Use the “Modified last” selection at the bottom left of the search form. One can also limit the list of items by JEL code and recency here.
IDEAS Search
Similarly, IDEAS allows to restrict search results to specific years. When looking up by JEL code, items are sorted with the most recent first.
EconAcademics
EconAcademics follows the latest discussion of research on the blogosphere. While it does not necessarily mean this is the most recent research, it is often the case.
The RePEc Blog 
If I can make a request without seeming ungrateful, please set up an rss feed for econacademics.org if possible. I’d love to get the summaries in my newsreader. Thanks for putting the website together.
For various reasons, a RSS feed for EconAcademics is not (yet) available. However, you may find interest in the widget that displays the last posts in a matter similar to a RSS feed.