EDIT:: OH! I misunderstood the question.

Um. I don't know if there is a specific genre. I can recommend:

• The House That Wouldn't Go Away author Paul Gallico
• The Black Stallion (and Flame) books author Walter Farley and by the way, things do get weird at very odd points.
• Watership Down by Richard Adams (waves hands hysterically Plague Dogs! aaaaaaaaaah wait, do these count? I mean, those stories aren't world-threatening...)

stares off into space for a while

• Katie Long and Siren author Tony Roberts (Imaginary Rock 'n Roll star's story)
• Kinsey Millhone Detective series author Sue Grafton
• Catch-22 author Joseph Heller

Probably many more, but of course now I am drawing a blank.