In our house it all depends on what it is and how we're feeling.
Typically, when it comes to pasta dishes, I tend to leave enough out for the following night (lasagna/spaghetti, etc), same goes for traditional meat & potato dishes. As for other things such as rice and noodle dishes (chow-mien, stir-fry's, etc), not so much, but again, it's all depends on how we feel.
Sometimes I'll plan meals for a few days where I make a variety of different dishes, and on these nights I prepare leftover servings that I can pack and freeze for a rainy day, and because there's a different meal being prepared and served each day, we eat something different each day.
One thing we don't do is eat leftovers for days on end. I find by day two, I'm leftovered out, and dear husband is the same.