Yes, Mark Cuban is a Jew. He owns the Dallas Mavericks NBA basketball team -- winners of the 2011 NBA championship.
Cuban's Russian Jewish grandparents changed the family name from Chopininski or Chabenisky when they immigrated to America. Cuban grew up in Mt. Lebanon, Pennsylvania, a suburb of Pittsburgh in a working class family.
In September 2002, Cuban married Tiffany Stewart, an advertising executive (who likely is not Jewish) in a private ceremony in Barbados.
The billionaire entrepreneur was charged in 2008 by the SEC with insider trading in what appeared to be a weak case.
Update: Case was dismissed but it can be refiled by the SEC (7/2009).
Update 2: Cuban is going after the SEC for malicious prosecution and has been granted discovery by the court (12/2009).
Update 3: Cuban on trial for insider trading September 2013.
Update 4: 10/16/2013 - a jury cleared Cuban of wrongdoing, making Mr. Cuban a winner in the civil case and delivering a blow to the federal agency that he battled tooth and nail for five years.