There is an old saying: "How do you eat in elephant? In small bites." The same rule probably applies to staying current with the ever expanding avalanche of medical literature. You can try the following approach:
1. RSS Feeds for Journals.
Subscribe to the RSS feeds of the "Big Five" medical journals (NEJM, JAMA, BMJ, Lancet and Annals) plus 2-3 subpecialty journals in your field of interest. Any of the many RSS readers would do. I use RSS Owl. PeRSSonalized Medicine by Webicina.com was one of the first services to arrange the medical journal feeds in a visually appealing way and make RSS consumption user-friendly. Feedly is one of the most popular online RSS readers.
Try to read the journal on the day it is published online, for example, NEJM and JAMA on Wednesdays, BMJ in Fridays, etc.
Listen to journal podcasts. Many applications are available for desktop and smartphones. All major journals have weekly or monthly podcasts.
3. Persistent Searches.
Subscribe to RSS feeds for "persistent searches" in Pubmed and Google. For example, choose a search term in your field of interest, run the search in Pubmed, then subscribe to the feed for the search. The same process can be repeated with Google News and Google Alerts.
Image source: U.S. National Library of Medicine.
4. Text-to-speech (TTS).
Use text-to-speech to listen to articles you do not have time to read. For example, you can save your articles in the Pocket app for Android and listen to them later.
5. Blogs and Twitter accounts.
Subscribe to high-quality medical blogs and Twitter accounts in your field of interest -- they often review many of the important new articles.
Here is an example of the allergists on Twitter:
This is a list of the allergists who are planning to use Twitter to post updates from the 2013 #AAAAI meeting. The list is open for edit, please feel free to add your own info.
How to stay up-to-date with RSS in medicine - presentation from the free Social MEDia Course http://j.mp/Hale12
Not a Medical Course, but a Life Course (somewhat vague advice) http://goo.gl/mDMsr - Here are 5 practical tips: http://goo.gl/n5rbw
Medical journals that use social media (spreadsheet). Body in Mind, 2011.
Image source: OpenClipArt, public domain.
Note: This is an update of a 2008 article.