It just depends on what it is. We never eat anything more than a week old. But most things are gone the next day. We really try to cook for just that day and lunches the next. Leftover pizza will get pulled out over several days. We'll have ham/turkey sandwiches for 4 or 5 days before we use any remaining in some kind of casserole.
My #1 rule is smell it! If there is even a hint of an off odor, it goes in the trash!
The other option is to freeze in portion size containers to have for quick meals and lunches since this will keep leftovers much longer.