Prince of Persia
As the title suggests, the game is set in Ancient Persia. The Prince is an orphan, living on the streets. One day, he scales the palace walls to catch a glimpse of the Princess, whose beauty is like the "moonrise in the heavens". His feelings are reciprocated by the Princess, despite their class differences.
The game starts with the Sultan of Persia being called away to war in a foreign land. Sensing opportunity, the evil Vizier Jaffar seizes the throne for himself. The Prince is imprisoned, since Jaffar has designs on the Princess. The Princess is also imprisoned and she is given a choice with an hour to decide: marry Jaffar or die. The Prince has an hour to complete the game by saving the Princess and killing Jaffar.
The twist is that the game is played in real time, so the Prince must quickly complete the quest without breaks. On some platforms it is possible to save the game at the start of each level, though the time limit still applies. The only way to lose the game is by letting the time expire. If the Prince is killed, the game will restart from the beginning of the level, or in some levels, at a mid-way checkpoint.