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.
Well can we start with Indian River State College in Florida?? Their Men's swimming team has 36 consecutive NJCAA national championships.