I've gotten into the habit of setting aside a 6-pack of every batch that I make with the premise of having a bottle for myself and one for my brother to have at 6 months, 1 year, and 2 years. On the whole, most of my beers have shown no particular improvement. They didn't get worse, but there was no real need to age. A few have shown improvement though, I did an American Amber that broke apart from the style a little that was very good young, but it also aged well and blended together nicely at a year and a half.
The biggest interesting one was a coffee Irish stout that I did. It was decent young, but at 2-3 months had lost most of the coffee flavor, so I hurried up and wiped out the second case. Turns out that proved to be a bad move. At 6 months the coffee taste as still gone. At one year, the coffee flavor was back and it tasted wonderful. At nearly two years, it was still wonderful but you could tell it hadn't improved beyond the one year for flavor.
I don't know that there is much of a hard and fast rule. It's more trial and error. I did a sweet Irish stout about the same time as the coffee one, very similar recipes, and it showed no particular improvement over time.