Horse Feathers

Professor Wagstaff: I'm Professor Wagstaff of Huxley College.
Baravelli: That means nothing to me.
Professor Wagstaff: Well, it doesn't mean anything to me either. I'll try it over again. I'm Professor Huxley of Wagstaff College.
Baravelli: Well, you didn't stay at the other college very long.

Horse Feathers is the fourth Marx Brothers film, co-written with S. J. Perelman, and arguably their first classic. Groucho Marx plays the incoming president of Huxley College, Quincy Adams Wagstaff, who with his usual partners in crime confronts a win-at-all-costs football game with the rival school, Darwin. The bad guys have hired ringers, pro ballers posing as student athletes, and the campus widow is on the make and out for the secret Huxley playbook.

The whole thing is, admittedly, an excuse for the usual Marx family lunacy. It lacked the satirical edge of Duck Soup and the social relevance of A Night at the Opera, but is forever beloved by college professors for its musical statement of administrative purpose: "Whatever it is, I'm against it!"

Tropes used in Horse Feathers include:

Always Gets His Man -- Invoked in song by Professor Wagstaff.
Banana Peel -- Harpo drops a whole bunch of them to trip up the opposing football players.
Big Game
Breaking the Fourth Wall -- Groucho, during Chico's piano playing:

Groucho: I've got to stay here. But there's no reason why you folks shouldn't go out into the lobby 'til this thing blows over.

College Widow -- probably the only movie centered around this Forgotten Trope that people still watch.
Fruit of the Loon -- Harpo snacks on a banana with a reclosable peel.
Getting Crap Past the Radar -- (Pointing to the backside of a horse) "That reminds me, I haven't seen my son all day."
- Also (after renting a canoe), "I wanted to get a flat bottom, but the girl in the boat house didn't have one."
- "For you, I'd make love to a crocodile." As noted in Having a Gay Old Time, the film came out at the time that this phrase was transitioning from meaning "flirt" to "have sex." Groucho definitely knew what he was doing.
Hurricane of Puns -- "I'd walk a mile for a calomel." Half of the puns are now pretty dated, but the other half will still leave you groaning.
"I Am" Song -- Wagstaff's "I'm Against It" and "I Always Get My Man".
MacGuffin -- the playbook, which Darwin College wants to steal, because they really want to win a football game for some reason. These are the kinds of details that don't matter in a Marx Brothers movie.
- The antagonist mentions that's he's bet rather heavily on the game, but it's never really brought up again.
Marry Them All -- inverted. The College Widow marries Groucho, Chico and Harpo all in the same ceremony.
Missing Episode -- several minutes of the movie were either cut or damaged, and thus Lost Forever (in a cinematic sense). The movie actually ended with the four brothers playing poker while Huxley College burned to the ground.
- Actually, while there are several minutes of the scene in Connie's bedroom which were sliced to ribbons by the Hays Office and are indeed Lost Forever (hence the many abrupt cuts in the film as it survives today), the bit about the college burning to the ground was an alternate ending which was planned, but as far as I know was never shot.
  - It's fairly certain the fire sequence was shot since photos of the scene exist, but whether it was ever included in the released film is a different matter.
Old-Fashioned Rowboat Date: Groucho has a rowboat date with the College Widow, who is trying to seduce him to steal information about an upcoming football game. The dialogue is anything but chaste, and the date ends with her falling into the water and Groucho wisecracking rather than saving her. Also, she was the one doing the rowing while Groucho sat under the parasol and sang to her.
The Password Is Always Swordfish -- the Trope Namer, if not the Trope Maker. There was a scene in the film where Harpo entered the speakeasy with his own brand of Sign Language (in this case, running a fish through with a sword and presenting it to the doorman).
Shout-Out -- to Charles Darwin and his advocate Thomas Henry Huxley.
What Happened to the Mouse? -- Zeppo's character disappears prior to the end of the film. His subplot was meant to have been wrapped up during the Missing Episode mentioned above.