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1.
Regional to Chicagoland, references the large ethnic Polish-American population, usually blue collar and first generation born. Not often used as an insult, but usually out of affection and ethnic differentiation, as Chicago is both a large melting pot, as well as home to the largest Polish population outside of Warsaw. A more derogatory term is Pollock.

Most well known stereotype exhibiting a Grabowski is the Saturday Night Live skit, "Da Superfans," which makes fun of the Chicago accent, love of "Da Bears," "Da Coach," "Ditka" and love of Maxwell Street Polish Sausage, all of which a proper Grabowski is known to love.

Possible etymology might reference Jim Grabowski, the star running back who played at Taft High school on the Northwest side of Chicago, then starred as running back at the University of Illinois Urbana-Champaign. He played professionally for the Green Bay Packers and the Chicago Bears in his final season, from 1966-1971. He then went on as a radio color analyst for the Illini, until the 2007 season. It is unlikely he had the accent on radio.
Oh man, last night, I went to this party on the Northwest side, and there were just tons of Grabowskis. Fun times.
by MistahMeätface November 21, 2009
 
2.
A Texas Hold-em poker hand of 2 face down starting cards consisting of a King and a Three.
Marc went all-in with the Grabowski.
by Mr. Corruption March 11, 2005
 
3.
a hott girl with a nice bod and likes to shizzle guys' nizzles
The Grabowski loves long walks on beaches and hott guys.
by Urlover November 13, 2003