You could argue that 3D and cinematic games that were brought forward through the success of the Playstation and adoption of the CD Rom on PCs killed a lot of genres and eliminated the "Hard-Core" videogame market ... Players no longer needed the complicated puzzle solving skills that adventure games required, nor did they require the lighting fast reflexes of adventure games, they now just needed the ability to stomach the engrish dialogue of cut scenes in order to be a good gamer.
In reality the genres died because of stagnation, they evolved into something different, or their appeal was dependant on a lot of external elements. Adventure games (for example) were loved because they were heavily storybased, and a lot of the challenge came from the limitations of the system (many people hated the move from a text-based to point and click interface); in a lot of ways, the elements people loved about adventure games worked their way into every genre.
The Nintendo DS and Wii will not kill any genre which is strong enough to be worthy of surviving.
