An example of a story where the character has one experience and the reader another--
Never Let Me Go (Ishiguro). This was just released as a film. The book is in first-person.
Don't want to spoil it (though suspense isn't the point), but the main character thinks she is in a book about going to a boarding school and adolescent relationships. But rather quickly the reader is in another story, about children being exploited and the intractability of fate. The great tension here is that the main character accepts as a given what the reader instinctively resists.
What are other examples where the author wants the reader to feel something other than what the POV character feels?
This is no big thrill in omniscient, you understand. With omniscient, the reader is "above" any characters, and so expects to feel more or other (ironic detachment, amusement). But in deep POV (or first-person), the separation in experience might be more subversive, as it's unexpected. (We're in the head and body of the character, feeling what he feels.)