In general relativity, the future light cone is the boundary of the causal future of a point and the past light cone is the boundary of its causal past.[Wikipedia]
From the moment of my birth, light [that I could have influenced] has been expanding around the Earth and light [which could influence me, from an increasing distance of origin] reaching it -- this ever-growing sphere of potential causality is my light cone. Today... My light cone contains 61 stars. Beta Leonis will be reached in in 5 weeks.
(Data taken from the utterly excellent An Atlas of the Universe, which has maps from the solar system out to the the Local Group and beyond. There's a lovely 3d map of stars within 50 light years, the data from which is used here. If you have data for beyond 50 light years, please let me know and I'll add it -- until then it'll only work for people born after 1954.)
To get a syndicated feed of stars within your own light cone and notification of the next to be enveloped, fill in the form to go to the subscription url. Copy-and-paste the address from your browser into your RSS news reader.
...or make the feed yourself. The URL is http://interconnected.org/home/more/lightcone/rss/?d=yyyy-mm-dd
Bug reports to Matt Webb (homepage). Run your own RSS feed or includes with dodgy Python scripts here.