But in some ways, it's easier to excise characters from the story than it is to make them respond in a rich and enjoyable fashion to all the things the player might want to do. The fact the rather clumsy interaction and wooden interlocutors in Façade have been noted for their responsiveness and human qualities underscores the problem. Moreover, good characters have arcs, and it's tricky to craft compelling character arcs outside a linear story.
The problem is particularly acute with a specific character present in every game: the player character. In a good adventure story the protagonist should drive the action, and in any self-respecting game, the player character should be the protagonist. But the more the player's "character" becomes integral to the story, the less the player is able to define the PC because the game's design will fix the character's role in the story (regardless of dialogue trees and alternate endings).
Turning the player into a passive audience dissociates him from the PC in a way that cleaves the game into two parts: playing a game and watching a story. This loses the best thing games can offer: the chance to be a hero (or villain). Attempting to infer a personality for the character, on the other hand, can force the designer to put fairly bland dialogue in the PC's mouth.
So what's to be done?

Down in Back
Although it's worthwhile to try to find a way to make character-driven stories dynamic and responsive, there's an obvious alternative: Move storytelling away from the character-based model by pushing any fixed, character-driven aspects into the game's back story.
In almost every genre where storytelling forms more than a superficial part of the experience, there are games with compelling settings and interesting narratives that don't rely on characters to drive the action. Consider Myst, Daggerfall or X-Com. While these games might feature characters, the characters were typically part of the back story, and the player's avatar was the one pushing the action forward.
In each of these games, the designers fitted a story to the game and to the engine's limitations. Myth's story, for example, is one of war, and it compares favorably to the stories in RTSes that tried, uncomfortably, to tell stories about characters using an engine suited for depicting impersonal hordes of soldiers.
