As a young man, Robinson Crusoe goes to sea against his father's wishes and lives to regret it. In spite of promptly being shipwrecked he goes again, and finds himself enslaved by the Moors for a year before escaping. He ends up in Brazil and becomes a well-to-do plantation owner before his greed gets the better of him and he once again ends up shipwrecked, this time on a small Caribbean island. Being the only survivor, he manages to save what he can from the shipwreck and builds a safe shelter. He plants crops, domesticates wild goats, and learns to be comfortable over the nearly 30 years he spends there, most of it alone. And parts of the story are highly religious in nature as he eventually develops a personal relationship with God.
The Mysterious Island isn't quite as well-known but also deals with castaways on a deserted island. Five Americans being held as prisoners of war in Richmond, Virginia during the Civil War hijack a hot air balloon during a terrible storm and end up in the South Pacific several terrifying days later. And you couldn't pick better men to be marooned with as their ingenuity and resourcefulness help them to survive on the island and establish a bit of civilization. The mystery of the island is several unexplainable events that happen, often at the most crucial and fortunate times. It's actually a sequel to Twenty Thousand Leagues Under the Sea, but for the most part there aren't many connections and they're actually very different books.