How can I tell whether a beer will improve with age? Most mass-market beers come with expiration dates, and cease to be good for drinking if too much time has passed since they were brewed, even if they've been stored in unopened containers and good conditions. Some major breweries even have long-running advertising campaigns about the freshness of their products.

Other beers improve with age. What qualities make a beer suitable for cellaring or bottle-conditioning? How can I know whether a given bottle of beer can be aged, short of looking it up online?
There are a couple of considerations, although this is far from a complete answer.

First, a stronger (higher ABV) beer will tend to cellar better, as the alcohol can act to help prevent oxidization.

Second, a beer with less emphasis on hops, and more on malt, yeast, or other characteristics, will be a better candidate, because the qualities that hops impart will fade in a fairly short time.  This is why your IPAs and such should be consumed sooner than later -- the character is primarily in the hops.

The purpose of cellaring a beer is to see its improvement over time.  Some may stay exactly the same, which others will change.  I think the answer there lies in whether there is still active yeast or bacteria in the bottle, and whether there is anything for them to chew on.  Some styles (lambics, for example) are far more prone to this, but I don't think there's a hard and fast rule that one couple follow.