The police radio in NFSMW is really neat. They would describe the make and color of the car you're driving, what area you were in, respond to certain actions you do (like crashing, stopping, hitting a police car, etc.), and also communicate with each other during the pursuit.
Ratchet and Clank cleverly masks loading screens with the scene of you traveling to the location you're going towards.
When you swim underwater in Banjo Kazooie the level music transitions to an underwater version of it.
In Super Mario Sunshine you can glance at some of the later levels in the background. Such as in Bianco Hills you can see Ricco Harbor down below if you look over the walls of the level.