For me, aging beer tends to make it smoother and more complex (probably because I seem to be able to taste more of the subtleties in aged beer as the aggressive notes diminish). Given this, I look to bigger beers with some "roughness" for aging - all of the examples previously given match that criteria more or less. I especially like to age beers that have been in wooden spirits barrels (bourbon, rum, rye etc) to let those aggressive flavors smooth out. And you don't normally see "small" beers aged in wood to begin with.
As to how long, that depends on the beer and your preferences. I think it's best to put away several bottles of the same beer and then taste them over the months/years (more quickly for the "smaller" ones), so you can taste the progress of the aging process. You're also less likely to "over-age" that way, too. Temperature plays a big part in the timing of aging; as I recall chemical processes tend to double in speed for every increase of 10 degrees C or 18 F, so beers will age more quickly with warmer ambient temps. But I'd guess that, so long as the storage temps aren't extreme or variable, anything between maybe 50F to 75F or so should be OK.