Army's traditional rival is Navy, whose nationally televised game is normally shown on whatever weekend the more popular teams don't happen to be playing (typically early Dec). Its a decent draw, normally played in Giants Stadium, JFK in philadelphia, or one year head scratchingly in the Rose Bowl
Modern recruiting and the requirement of a service obligation after graduation has now unfortunately reduced Army Football to a laughingstock of the CFL. (Which some recent bright spots... close losses to Alabama and Auburn in bowl games) At one point they set a record of losses in college football by going 0-13.
Have to give some credit to Army Football guys though cause they have to attend class, have to take their own tests, and have to do all the crummy stuff the other academy guys do.
I don't know how in the heck Navy football pulls off these good teams lately and good for them! But Navy seems to get the media breaks. They get Top Gun, Army gets Blackhawk down. They get Navy Seals and Army gets an ESPN movie about the Army Football cheating scandal!
Contrary to what you might have seen on MASH, nobody in the real Navy or Army give a crap about the Army / Navy game unless they are former players. Days off are given for the Super Bowl in the Army, not the Army/Navy game... what does that tell you.
"I need a man for a tough and dangerous mission, I want a West Point Football Player" -- Some famous WW2 general (caveat- he was an alum)
Props to Texas A&M, Notre Dame, The Citadel, Norwich, Air Force, and VMI for their fine record of military service in our nation's wars