I make a conscious effort to use up leftovers before they have to be thrown out. My family is more likely to eat them, however, if they're re-purposed into something new instead of simply warmed over. From time to time, I post "Use It Up Tips," ideas for turning boring leftovers into something more exciting.
One of my favorite way to use up leftover potatoes is to make fried potatoes as a side for another meal. I melt butter in a skillet, cut the potatoes into thin slices, sprinkle with dried onions and/or seasoning salt, and fry until crispy. I usually use baked potatoes (and often make 1 or 2 extra just for the leftover possibilities), but have used potatoes that have been cooked with meat, or boiled potatoes.