Here are some of those notable films:
Lord of the Flies (1990)
This 1990 film was the second adaptation of the novel written by William Golding. Although there are some significant differences from the book, the film follows a group of young American cadets who end up on a island after their plane crashes in the ocean. With no adult supervision, they try their best to get along with each other but end up splitting into two camps; one did their best to be as civilized and organized as possible, and one reverted to primitivity. The two camps then clash as the chances of survival become smaller.
The Blue Lagoon (1980)
The Blue Lagoon is also based on a novel by Henry De Vere Stacpoole. A young Brooke Shields and Christopher Atkins play two cousins who reach a tropical island after surviving a shipwreck. After their only adult companion dies, the two then try to survive on their own. After years have passed and as they reach their adolescence, they slowly begin to fall in love and discover their sexualities. With their lack of experience in sexual knowledge, they become unwary of themselves which eventually lead them to conceive a child.
Swept Away (2002)
Directed by Guy Ritchie, Swept Away is about a rich and arrogant woman who finds herself stuck on an island with the ship's first mate, who she loathes, after a storm turns their cruise into a nightmare. Played by Madonna and Adriano Gannini, the two fail to get along especially when Adriano's character, Giuseppe, gains the upper hand. But things slowly start to fall in place when they realize they have feelings for each other.
Cast Away (2000)
When a FedEx employee finds himself alone on a deserted island, he uses the items in recovered packages to help in survival. With his inanimate friend, Wilson the volleyball, he managed to live off of the island's resources for four whole years. But as he tries to leave the island on a raft he built, Wilson accidentally drifts away from him after a series of unfortunate events in the ocean. Although this brings him grief, he was later found by a cargo ship which brought him back to civilization.
These films are definitely a must-watch along with a whole lot more (i.e. Nim's Island, Survival Island, etc.) and I have to warn you, some of these a real tearjerkers.