I have seen much older in stores, etc. (don't know for sure what the oldest was), but the oldest I can remember tasting was a 1970 Chateau d'Yquem, which I received as a gift from my soon-to-be father-in-law. It was excellent...definitely more than "rotten, fermented grape juice"! Would I know the difference between it and, say, a 1971? Possibly not--I'm not that much of a connoisseur. But it was substantially different from newer Sauternes I have tried. Ditto with a 1978 Latour that I drank last year.
Note that not all wines age well. The vast majority should be consumed within a few years of bottling. Certain reds, however, notably cabernet sauvignon (and therefore the great reds of Bordeaux, like Latour, of which cab is usually the principal grape), age very well, as do many sweet whites such as Sauternes (like the Yquem I mentioned above) and riesling auslesen/beerenauslesen/etc., and of course vintage port, which is known in particular for its longevity. But your average less-than-$10 bottle (or box, heaven forbid) of wine might not taste so good after 5 years, let alone 20 or 30!
Common sense is not so common. -Voltaire