There's no single answer to that question. Some wines are very long-lived, and may go 30 or 40 years after the "wait until" date, whereas others are over the hill within a few years. It depends on the makeup of the particular wine -- the balance of fruit, tannin, acid, and so forth, as well as a particular wine's track record. Rely on the experts for that information, at least until you develop some sense of such things for yourself -- which takes a long, long time and a lot of experience.
Longevity also depends a great deal on how the wine is stored. If allowed to rest in the dark at a constant 55 degrees or less and about 60% humidity, most wines will age slowly, but if kept at room temperature or in bright light, they die an early death.