Buzz (175) has won at least one regional/field for the past 10 years. Except that one year, when they won the Chairman's award (this was prior to the existence of the Regional Chairman's award).
Team Hammond (71) has 5 Championship/National Finals appearances (1997, 2001, 2002, 2004, 2007), with 4 Championship/National wins (1997, 2001, 2002, 2004). As Dave Verbrugge pointed out, Beatty has now graduated two freshman classes who never saw a Championship win, but they have yet to graduate one who hasn't seen a Championship finals appearance, a feat no other team has come close to matching.
Hyper (69) had quite the 2004. Their robot
never lost a match in two regionals. They tied a match or two, and their elimination alliances lost a match or two when HYPER was sitting out.* Unfortunately, they elected not to go to the Championship that year, as if they did I'd imagine they were on crash course with the Beatty Beast. Obviously, it's impressive, but even more uniquely, it didn't have a collecting mechanism for the 5 point balls. Instead, it was well equipped for the 50 point bonus for hanging from a 10 foot chin-up bar, and capping the goals with the big yellow Doubler Ball (which, doubled the points value of the balls in that goal). Does anyone have a better picture of HYPER from 2004?
Hyper also took a nasty spill that year. One of the biggest audience reactions I remember from the past 6 years.
*In 2004, matches were played with 2 robots on the field, but alliances consisted of one team, so one robot was left sitting out.