The first rule of aging beers is that there are no rules in aging beers.
First, on the subject of what beers to age:
Hop aroma and flavor definitely fades over time. Harsh alcohol flavors also fade over time. Malty flavors develop more complexity. Higher alcohol beers lose some of their "hotness" and become more rounded and balanced, but even lower alcohol malt-forward beers change over time. So, the generally considered best candidates for cellaring and aging are stouts and barleywines with their big alcohol and low hops. But, this doesn't mean that you can't age an IPA and see what it's like in a few years.
Now, on the subject of temperature:
At refrigerator temperatures (in the mid 30's F) beer will age slowly, and typically does not lead to the development that most want in aging beer. Too warm (mid 70's F+) and the beer will age more quickly and also not really produced what most consider the best results. Generally, a constant temperature somewhere in the range of 50's F is what is considered ideal, much like wine.
So, ideally, you get some nice barleywines and stouts, and put them somewhere at a constant 55F with no light and forget about them for a few years, come back and find that they're much better than you remembered, and much better than what the same beer brewed within the last few months is.
But!! You don't have to play by the rules. Try aging different beers, try different temperatures. Drink barleywines young!
I kept a few years of Bell's Hopslam and did a vertical tasting this year. Three years of the same beer, 2011-2013. All aged bottles were kept together, and much of that time was spent at refrigerator temperatures. What did i find out? The 2013 was a great beer, fresh with lots of hop aroma and flavor. 2012 was probably the worst out of the group, most of the hops had faded, and without them the beer just wasn't the same. An interesting thing with the 2011 though, while the same as 2012 with the lack of hops, the rest of the beer really started to come together. Without the hops it really didn't taste much like the 2013, but the malt and honey in the beer really started coming out and coming together.