None in football one in baseball
Lawrence High School in Lawrence, KS has 105 total state championships.
Stroman was a 5 A school, they even won a 5A baseball state championships in '85 or '86.
In 2008, Arizona State won the Softball College World Series. They were undefeated in the series. They finished their season with a record of 66-5.
According to Wikipedia there has been 5 state championships
Here are a few teams who hold the record for nost state championships in particular sports: Track & Field: Minneapolis Central, 13 championships Softball: St Bernard's St Paul, 7 championships Vollyball, Girls: Robbinsdale Armstrong, 7 championships Hockey, Boys: International Falls and Roseau each have 7 championships Football: Mahnomen, 6 championships See related links for Minnesota State High School League Records for various sports.
Washington High School of Sioux Falls, South Dakota has 39 state championships, they won 14 straight from 1952 to 1965
East Grand Rapids High School in Grand Rapids, MI as of November 2010 has 115 State Championships.
Ohio State has 5 solo championships and 2 shared championships that the school considers titles, so they have 7 total.
Edina HS in Edina Minnesota has 134 MSHL State Championships, 143 total