Off the top of my head:
SCV has made every final.
Blue Devils, in ever since 1974.
Cavaliers only missed a couple of times in the 1970s.
Cadets, in since 1980 and made a couple of 1970s finals.
Phantom Regiment, in ever since 1974. (These five are the ones with the 39 consecutive years.)
Crossmen first made it in 1977. Early 80s, check. Early 90s, check. Early 00s, check. In now, check. Yes, they have each decade covered.
Spirit first made it in 1978. Early 80s, check. 1990, check. Middle 00s, check. Early 10s, check. Count them in.
Madison has never been out two years in a row, so they must be the 8th such corps.