Full-bodied, full-flavored cigars benefit most from aging, IMHO; many of them have strength to spare, and mellow out a bit with age.
Milder cigars may benefit from a year or two of aging, but they may also become too mild. When I was just starting out with fine cigars, I heard about something from Villazon that had been "forgotten" for several years and bought a couple of bundles. Some of the people who had tried them guesstimated that they had been aging anywhere from 10 to over 15 years; I can tell you that they were so mild as to be almost flavorless, but the nicotine had out-migrated to the cello -- both around the individual sticks and the bundles themselves -- to the point that you could scrape the dark yellow coloring off with a fingernail. (The cigars still had so much of their essential oils, though, that they could serve as lip balm.)
If you've ever bought Consuegras, you probably know that they are supposedly seconds of Hoyo de Monterey, Punch and other fairly powerful cigars; you probably also know that a bundle may contain "seconds" of more than just one brand. I aged a couple of bundles (No. 9s, I think) for a few years, and not only did they mellow, but -- perhaps because I did not open the bundles more than necessary to try one from each ROTT -- they all tended to taste very much alike, mostly like well-aged Hoyos or strong-ish Excaliburs.
Had enough balls to last and smoke like a good cigar. Sadly it was a one-off in my humidor. Last of the last. I wanted to smoke another one but none left. 