I had hoped to put together an academic geneaology, mapping out the Binford patriline. Unfortunately, it is very hard to find information about his students on-line, and my personal knowledge is patchy (and highly incriminating of my identity, not that most of you don't know that already!). I was able to find the following list of Binford's students at the University of New Mexico, which represents the bulk of his career.
Alan Osborn (Nebraska State Museum)
R.F Schalk (Cascadia Archaeology)
Richard Chapman (New Mexico Office of Contract Archaeology)
Robin Torrence (Australia Museum)
Robert Hitchcock (Michigan State University)
Larry Todd (Colorado State)
Robert Hard (UT San Antonio)
Mark Stiger (Western State University, CO)
Michael Smyth (Rollins College)
Mary Stiner (Arizona)
Steven Kuhn (Arizona)
James Enloe (Iowa)
Dan Amick (Loyola)
D. Oswald (Prescott College)
RP Mauldin (UT San Antonio)
Mark Lycett (University of Chicago)
My apologies to those whose affiliation I do not list, or if I have it incorrect. Many of Binford's students are working in CRM or government jobs, and have been very influential through their publications and interactions with other scholars. I didn't include those affiliations here, just because my original intent was to put together an academic pedigree chart, so I was interested in Binford's students' students. That turned out to be impossible, but just from this partial list of his students, it's clear he's left a significant legacy.
If I remember correctly, Bob Whalen (University of Michigan), Jim Brown (Northwestern), and Stuart Streuver (Northwestern), were also students of Binford's at Chicago. I don't know any of his students from SMU. Clearly, the list above is just the tip of the iceberg.