I like the idea of game series based around a common group of characters or a common setting. As with the Star Trek example, they don’t necessarily have to be direct sequels. The Jeeves and Wooster stories occasionally refer back to past events, but can still be read in any order. The same goes for Sherlock Holmes. It definitely helps that the status quo resets at the end of every episode.
The AGS community had a project called Reality-on-the-Norm in which the setting (a small town) remained the same, but with each chapter adding new characters and depth to the world. I’ve often thought it would be fun to do something similar in IF.