When it appears that Gilligan will be challenged to a death match for a girl whose life he saved, the Professor, Mary Ann, and Ginger (possibly the only three in the hut) agree that they will fight and die with him rather than simply letting him get killed.
Mr. Howell, of all people, gets one of these in this episode. When he overhears the Skipper and the Professor seemingly plotting to kill Gilligan themselves (the Professor is actually helping Gilligan fake his death), he is outraged and attempts to find Gilligan and help him escape. When the Professor and the Skipper arrive to administer their knockout potion, Howell takes a swing at them.
Gilligan gets one at the end of "The Big Gold Strike" when, for once, he's the only one not responsible for the failure of the latest escape attempt because he's the only one who didn't smuggle gold on the life raft, which caused it to sink.
He gets another one in "The Chain of Command." To summarize - the Skipper has been training Gilligan to succeed him if anything should happen, and Gilligan being Gilligan, it hasn't been going too well. Then the Skipper disappears and it looks like he's been kidnapped. Gilligan gets the Castaways behind him - in spite of the fact that some are not too keen on the idea - and sets a trap to catch one of the Skipper's kidnappers. It turned out to be unnecessary , as the Skipper disappeared for a while as a secret test for his successor, but even so.
He gets a third in the episode "Seer Gilligan". In addition to growing pineapples and coconuts, the island also apparently grows mind-reading seeds. Gilligan brings some back to camp for everybody. However, this soon causes trouble as the Castaways hear the uncomplimentary things that they have never communicated before. Seeing the whole group snapping at one another, Gilligan runs back into the jungle and burns the bush with the mind-reading seeds. Even the other Castaways recognize this as a Moment of Awesome for the awkward first mate.
In "Topsy Turvy", Gilligan fakes out the headhunters who have captured all the other Castaways by getting them to drink a potion the Professor made to fix his eyesight which made him see double.
Gilligan's actor Bob Denver got a real-life one, when he went to the show's producers and forced them to properly add Russell Johnson and Dawn Wells to the opening credits; Wells has said she didn't find out until years later that he had done this.
Ginger manages one in "Ship Ahoax" when she pretends to be a fortune-teller in order to alleviate the Castaways' 'island madness'. Things go a bit too far when everyone buys into it, and asks her to predict the exact time of their rescue. In order to restore some reason to the situation, she passes each Castaway a note: "Please don't tell anyone I'm a fake." The hoax is dispelled with no one feeling betrayed, and life returns to normal. As it turns out, a ship passed very close to the island at exactly the time Ginger 'predicted' but Gilligan was called away from setting the signal fire by the Skipper.
In one episode, Ginger pretends to seduce Gilligan in order to pickpocket his lucky medal, as the Professor had asked for all metal on the island to craft an anchor for their latest raft. We clearly see her take the medal. As she's about to leave the hut, Gilligan reveals to her rather smugly that she failed as he dangles the medal like a yo-yo in front of her.
The women get a collective bunch in "St. Gilligan and the Dragon." As the episode opens, Ginger and Mary Ann angrily "go on strike," refusing to cook or clean until they get a hut of their own, which the men have promised to build them for weeks (put yourself in their position: having to share a communal hut with four other men!). Mrs. Howell joins the protest when she points out that she's been asking Thurston for a private hut, too (which is again understandable for an older married couple). The Professor, in a surprisingly nasty moment, tells the women that they'll have to wait, and furthermore that men should make all of the decisions. That kicks off the Awesome:
Mrs. Howell demonstrates a surprising knowledge of mythology and theatre when she brings up Lysistrata, and convinces the women to follow her example by moving to the other side of the island until they get their huts. The girls happily agree, with Mary Ann citing both her duties running a farm and her experience as a Girl Scout, while Ginger discusses her time with a Boy Scout (who apparently "taught her a lot").
Despite struggling with a heavy sledgehammer, the trio is able to build a hut within one day. Mrs. Howell even helps them construct it; contrast that to her husband, who refuses to help the men with any of the labor.
The men crack first and try to get the women back by scaring them with a monster costume. Ginger (who'd sneaked back to the camp to get a smaller hammer) overhears the plan and tells Mary Ann and Mrs. Howell. They successfully beat the men at their own game by being "scared" of the monster...and reacting by grabbing sticks to bludgeon it to death.
When the men decide to give up and ask for the women to come back, Thurston goes first, figuring that he can use sweet nothings on Lovey to woo her. When he sticks his head in the tent, he's promptly doused with two buckets of cold water and called a "peeping Tom."
“The Hunter” is a group moment. The rest of the castaways all do their best to help Gilligan evade Kincaid, which results in his offscreen Villainous Breakdown. To elaborate, after returning to civilization, Kincaid wins a target-shooting competition with a perfect score, but immediately after suffers a nervous breakdown and winds up institutionalized, constantly repeating one word: “Gilligan. Gilligan. Gilligan.”