Your ship has crashed and you are rescued onto a ship full of girls!
This leads to Multiple Endings, though some Dating Sims make it possible to see several of these "endings" in a single playthrough.
Some Sim Date games have been made into Harem anime, though the result is usually nothing special due to the removal of sex and the fact that the narrative can no longer focus on any single character.
Because there is almost no market for true Dating Sim games outside of Japan, it's a frequent misunderstanding among western gamers that "Dating Sim" is the general term for all ren'ai (romantic love) games.
In fact, many romance games are Visual Novels, which is a much different game style.
(See for example, the difference between the series, which is very close to a Visual Novel style of gameplay, and the DOA Xtreme series, which is the closest thing to a true Dating Sim with mass-market appeal in the US.) If the game plays out like a Choose Your Own Adventure, that's a Visual Novel.