It varies widely depending on many factors - sanitation and packaging conditions (e.g. amount of oxygen), temperature, and beer style being some.
From a beer style perspective, some general rules of thumb are:
1) darker beers will age better than lighter beers
2) bigger beers age better than smaller beers
3) hop character drops off relatively quickly
So, for example, light, wheat beers and ipas are best when fresh (a few months), but a big russian imperial stout, if stored properly, will be fantastic years down the road.
I don't think you can put a definition on "Big". It is a spectrum, from "Smaller" to "Bigger". Some might say 1.060, others 1.070, still others 1.080 and up. THe way I see it is that a light-colored, hop-forward beer with an OG of 1.045 will not age particularly gracefully compared to a dark, roasty beer with an OG of 1.080. How things fall in between is difficult to predict.
Most aging should come before cold storage. That is the temperature at which any yeast still in your bottles will function best. They can aid in aging. Most people recommend cellaring between 50-60 degrees for any longtime storage.