"Sparticle" is a merging of the words supersymmetric particle.
Supersymmetry, one of the cutting-edge theories in current high-energy physics, predicts the existence of these "shadow" particles. According to the theory, when the more familiar leptons, photons, and quarks were produced in the Big Bang, each one was accompanied by a matching sparticle. This state of affairs occurred at a time when the universe was undergoing rapid phase change, and theorists believe this state of affairs lasted only some some ten trillionth of a ten trillionth of a nanosecond (10 e-35 seconds) before the particles we see now "condensed" out and froze into space-time. Sparticles have not existed naturally since that time.
However, if theory is correct, it should be possible to recreate these particles in high-energy particle accelerators. Doing so will not be an easy task; these particles may have masses up to a thousand times greater than their corresponding "real" particles. Current colliders do not have the power to create these supermassive particles, but the Large Hadron Collider, now under construction at the CERN site in Switzerland, will be able to achieve collisions in the 14 TeV (terra-electron-volt) range, more than adequate to determine if these superpartner particles exist.
Additional information:
Argonne National Laboratory => http://www.anl.gov/OPA/Frontiers2000/b5excell.html
Large Hadron Collider => https://edms.cern.ch/cedar/plsql/cedarw.site_home
CERN homepage => http://public.web.cern.ch/public/
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