Did the rest of the cast let the Howells goof off because they were rich, because they were older than the other Castaways, or because they were useless and would get in the way?
In "Mr. and Mrs. ???", the Skipper enlists Mary Anne and Gilligan to help him practice officiating a marriage before he tries it on the Howells. Was this simply because he thought they were the only two he could get to do it (given the Professor's awkwardness with romance and Gilligan's bashfulness when Ginger tries to kiss him) or because he wanted to nudge them towards becoming a couple?
Ear Worm: The theme song. As Achewood pointed out, Emily Dickinson's "Because I could not stop for Death" fits the theme song... as do "Amazing Grace", "Auld Lang Syne", and the first verse of the first English Pokémon theme, which is not surprising since they all use Common Meter.
The pilot's theme, featuring Sherwood Schwartz on vocals, is also quite catchy. That theme, and most of the series' early incidental music, was written by John Williams. Yes, the John Williams.
Which is not quite as out-there as it sounds: it's a commonly taught piece of sitcom-writing advice that main characters should embody as many of the seven sins as possible, because it gives them something to want and work for (driving the plot) but also a reason we enjoy seeing them fail (because their desires are ignoble).
They end up being rescued in the reunion movies. So looks like that bad karma was worked off. Talk about Earn Your Happy Ending.
Expy: The Professor's character is very similar to that of Mr. Boynton of Our Miss Brooks fame. Originally, the Professor was to be a high school science teacher rather than a college professor.
Ham and Cheese: The whole cast to some degree, but Jim Backus as Mr. Howell in particular (and the character was immeasurably the better for it).
In "St. Gilligan and the Dragon", Gilligan mistakes a weather balloon for a ferocious monster. A few years later, The Prisoner featured a vicious monster that just happened to look like a weather balloon.
Hollywood Homely: Mary Ann. Dawn Wells was Miss Nevada 1959 and participated in the 1960 Miss America contest. She's also aged insanely well. Even lampshaded on The Simpsons when the network executive wanted someone "ugly" like Mary Ann, not "ugly ugly" like Moe. (Even though none of the other Gilligan characters ever referred to Mary Ann as homely; more the shy, Girl Next Door type.)
Ho Yay: In one episode both Gilligan and the skipper both think the other has been turned into a monkey. It Makes Sense in Context. What is the first thing they do when they see the monkey dressed up in the other's clothes? Strip it naked, of course.
Apart from that, consider the Skipper's way of addressing Gilligan as "Little Buddy."
Never Live It Down: Gilligan is so infamous for "always" accidentally ruining the Castaways' plans to get off the island that Just Eat Gilligan became a meme and then a trope. But a dedicated fan decided to watch every episode and make note of the number of episodes the castaways tried to get off the island and the number of those episodes where their plans were ruined by Gilligan. It turns out Gilligan bungles their plans in exactly 17 episodes. Which is still a lot, but it's less than half of the number of episodes the Castaways tried to escape, 37. More importantly, there were 98 episodes total. So Gilligan botched the Castaways rescue/escape attempts less than half the time they tried and in only a little more than a sixth of all episodes.
The Woobie: A lot of fans feel sorry for Gilligan. He's often yelled at or insulted by other people. Admittedly, some of this is for things he messes up, but he also does a lot of good things (performing much of the labor on the island and saving his fellow Castaways from various dangers) that get much less attention.
The Problem with Licensed Games: Why someone thought the show would make a good video game is one of history's great unsolved mysteries, but it could have produced a goofy but still somewhat fun and playable adventure game, in theory. What happened instead is held to be among the worst NES games ever released.