KYH puts it very nicely. For a long time I was very bad about eating leftovers, in large measure because to me the term has indeed always meant "eating yesterday's food reheated." Only in the last few years have I begun to learn how to treat everything left over (note space!) as an ingredient.
I have two big standbys on this: soup/stew and curry, in that order. Basically dinner on Monday becomes most of the solids in soup/stew on Tuesday, the liquid being broth usually made from the trimmings from preparing Monday dinner. On Wednesday the leftover Tuesday soup-stew is strained and added to some newly cut and sweated vegetables, the strained solids are added just to reheat, and then to this mixture I add broken-up curry roux. (I don't know if that's a familiar ingredient to most people, but you can't turn around in large portions of East Asia without bumping into this stuff. It looks more or less like chocolate, is basically spices and pre-cooked roux, and you dissolve it in very hot liquid to produce brown curry glop that is utterly unlike anything I have ever heard of in relation to South or Southeast Asia but is enormously popular in East Asia. My kids love it.) The curry is served over rice, and if there is anything left that actually does reheat extremely well in the microwave for lunch on Thursday. Last night was curry rice, and included the very last of the smidgen of dry overcooked turkey breast my mother gave us as leftovers. It wasn't dry this time, perhaps because it's been cooked in liquids every night for three days!
Another good one if your leftovers include really excellent broth of any kind is risotto. Start with a little freshly-sweated vegetables, use the hot broth to infuse the risotto in the usual manner, and as you near the end add the solids floating in your broth. Obviously not every kind of soup will work for this, but you'd be surprised at how good a hearty minestrone risotto can be.
Conversely, if you don't have small children to worry about, you can always smother things, Cajun-style. I love this, and so does my wife, but I can only do it once in a blue moon because my kids won't eat things with more than a dab of black pepper, to say nothing of full-on Cajun cooking. Basically you need four things: fresh vegetables, leftovers, broth of some kind, and dark roux. Cook the vegetables over high heat in a little oil, covered, stirring fairly often, until they're getting deeply brown and you can't unstick them from the bottom --- about 10 minutes. Add a little broth, deglaze, and add your leftovers. Continue cooking until the liquid has evaporated and it's all sticking again. Add all the rest of the broth and water if necessary to cover the ingredients by maybe an inch, and bring to a boil. Stir in the roux in generous spoonfuls, stirring until dissolved, until it is reasonably thick. Reduce heat and simmer for half an hour or so, stirring occasionally. When it's done, it will be quite thick, brown, and gloppy looking. The spices, by the way, should be added in stages: basically every time you add some new ingredient, add more spices. The spice mixture is a matter of contention and opinion, but I tend to stick by the recipes given in Paul Prudhomme's Louisiana Kitchen, which are complex and wonderful. Another great thing about smothered leftovers is that, like curry, it reheats amazingly well, in the microwave or on the stovetop, so it's one kind of leftover I for one don't mind eating as a leftover. In fact, like gumbo, this stuff generally gets better after sitting overnight in the fridge!