Lee Smallwood and Debora Katz (of the US Naval Academy) and I have
written a paper which describes how one can measure the
parallax of asteroids which pass close to the Earth.
You can
download a PDF copy of the paper.
The
CLEA Project
includes an exercise in which students measure the parallax of
an asteroid. It also includes a very handy set of tools
for doing these measurements yourself.
For a different aspect of parallax, look at these pictures
of asteroid trails taken by the Hubble Space Telescope: