The quickest way to get rid of leftover wine is to think of it as flavoured water. In many if not most recipes that call for water - especially stovetop recipes like sauces and stews - you can simply substitute wine for the water or stock that the recipe normally calls for.
We actually had a similar question recently: In what kind of recipes can I substitute stock for water? and I'd recommend you take a look at that, as many of the points there apply equally well to wine. Probably the best summation was in bikeboy389's answer:
I'd consider stock to be just another flavorful liquid (thanks Alton Brown), to be usable in exchange for others like wine, etc. You need to be conscious of the gelatin aspect and mindful that some substitutions will be more successful than others, flavor-wise, but it's always worth considering if stock might be a good substitute for any other flavorful liquid.
Just swap the terms "stock" and "wine" and you're good to go. Even though wine doesn't contain any gelatin, you actually do need to be mindful of the gelatin aspect when substituting wine for stock, because you might have the opposite problem if the liquid is supposed to thicken.
Similarly to stock, I also wouldn't recommend using wine in anything that you plan to refrigerate or freeze for a long period, for a different reason obviously - because it can go sour over time. So try to only use it in recipes that will be consumed in the near future.
Other than that, just experiment; whenever you're making a savoury recipe that calls for water or stock, try using some wine instead. You'd be surprised at how much character it can add to otherwise simple dishes. Some examples of places where you can replace some other liquid with wine:
- Rice or risotto
- Soups and sauces
- Deglazing a pan (for a pan sauce)
- Salad dressings (this is an especially good use for sour/fermented wine)
- Poaching liquids (for eggs, chicken, etc.)
There really are no rules, and any time you find yourself tossing plain water into a pot or bowl, you should keep in mind that you are potentially missing an opportunity to add flavour (which a good wine will add plenty of).