As a grad student at the University of Virginia I was able to join the
floor hockey club.  There were only about 3 or 4 other grad students
in the club, but it was open to all.  As for grad students on the regular
teams, UVa's football team has had two grad student starting quarterbacks
that I know of (Shawn Moore and Matt Blundin).  They both played while
undergrads, graduated in 4 years with 1 year of eligibility left, and
played one more year while attending grad school at UVa.  I have never
heard, however, of a walk-on grad student.
 
Pete Kester
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