One reason I like Southern Rhone wines is that aging is not really an issue. Most of these Grenache-based wines taste good right out of the gate, and the changes they go through after that are mainly a matter of taste rather than quality. On the other hand, because of low yields, old vines and good winemaking, you can usually hang on to even an inexpensive (but well chosen) Cotes du Rhone or Vin de Pays for eight to ten years without worrying that it will become undrinkable. You really can't say that for inexpensive New World Cabernet or Shiraz.
I reported on a 19-year-old Gigondas below, but there is a great deal of variation in Gigondas wines even from the same vintage. Santa Duc Gigondas impressed me as a wine somewhat similar to Goubert in youth; yet I drank most of my bottles a decade ago and even then some were beginning to show their age. Cayron, on the other hand, is a wine for keeping. I'm still enjoying bottles from 1980 and 1981; the 1986 tastes just right; and the excellent 1988 is still a bit aggressive for my tastes. Font-Sane, from my experience, is somewhat between Cayron and Santa Duc but tastes best to me after a decade or so of aging.
I rarely drink Chateauneuf du Pape before it's 10 years old, but that's because it's still a bit one-dimensional before that time, not because it's hard or tannic, as is the case with a good Bordeaux or Napa Cabernet. And vintage is crucial: 1993s need drinking now while most 1988s still have some time to go.
As for Cotes du Rhone Villages, I've had the greatest pleasure from aged Rasteau--even 12 to 15 years of age or older for wines such as Beau Mistral, Soumades and Queyrades. Aging seems to tame some of the aggressive black licorice/mineral elements in a way that's pleasing to me. Many Vacqueyras wines--such as Couroulou, Amourier and Montvac--also do well with eight to twelves years of aging. My favorite Vacqueyras at the moment, Monardiere's Calades, on the other hand, seems to decline rather quickly after five to six years in the bottle. From Cairanne, Brusset may be the best known estate (because of frequent mention by Robert Parker), and I have found that it needs to be consumed three to five years after the vintage date. Domaine l'Oratoire Saint Martin is a better wine, in my opinion, and ages better--although ten to twelve years is probably the best you can expect in a good vintage.
Aging with most Southern Rhones is mostly a matter of what you like. I found even Cotes du Rhones from the 2001 vintage were a little hard for the first year or two; those from 2003, however, were better in the blush of youth.