Beer is usually found in fridges in shops and supermarkets. At home, you would store it in the fridge as well before drinking. On the other hand, many liquor shops have stacks of beer cans outside fridges, and beer in kegs isn't usually refrigerated when it's transported.
What are the benefits of keeping beer refrigerated? Which kinds of beer should/must be refrigerated and which ones don't need to be?
Beer should be chilled to the proper serving temperature, which may vary according to ingredients and brewing methods, and even most of those are not set in stone, but can also vary according to taste.
Guinness, for example, has a specific serving temperature related to how it was traditionally stored in Ireland (Kegs in the "cold" room, which was often just a room carved out of the hill behind the pub or similar).
As far a why grocery and convenience stores keep it chilled, it's basically appealing to the "grab and go" drinker, who intends on consuming it in the very near future, or with a short transport. Often they are slightly higher price than if you were to go to a liquor store.
Liquor stores have much larger selection and inventory, and refrigerating everything would be cost prohibitive. The price is generally slightly less than the grab and go locations, although many liqour stores still keep some of the more popular and mainstream beers in the cooler as well.
For most commercially available beers, you can cool, warm and recool several times with minimal to no changes to taste. Some craft and/or home brews may be affected more by this process, but I don't know if there is any kind of a list available.
Heat and light are the enemies of beer.
If you have a "bottle conditioned" beer -- that is, one in which live yeast are still present -- then under warmer conditions, you potentially have active yeast. To some extent, this may just increase the carbonation and alcohol content. However, if most of the fermentable sugars have already been fermented (that is, converted to CO2 and alcohol), the yeast will start "eating" each other, which will result in some very "off" flavors (though nothing toxic). Under cooler conditions, the yeast will be only minimally active.
Regardless of whether your beer is "bottle conditioned" or not, the hop acids present from the brewing process don't respond favorably to heat or light. In particular, light can cause them to turn "skunky", which is why Corona -- with their clear glass bottles -- often tastes "skunky". Don't trust a beer in a clear bottle ... seriously.
Keep it cool; keep it dark; keep it upright (unlike wine).
To quote Strongbad, "A one that is not cold, is scarcely a one at all."
In supermarkets you will often see the same beers stored in refrigerated and non-refrigerated sections. Or you may be able to get a beer cold somewhere but only warm somewhere else. If you go to a large beer store you will see beer of every variety sitting in aisles. The general reason for keeping beer on ice in a store is so it can be drunk right away.
The one exception I can think of is bottle-conditioned beer. Beer where some degree of fermentation occurs in the bottle, giving it both natural carbonation and causing the flavor to develop over time. The flavors the beer will take on during conditioning vary based on warm or cold conditioning, and the beer will have a more limited shelf life. You will typically only see bottle conditioned beer as a product of home brewing.
When talking about the temperature to store/serve beer it is important to note that there is a difference between types of beer (and what we call beer in the UK and what people call beer in other countries!).
The Cask Marque website has a simple page denoting the various temperatures that some types of beer/ale should be stored at. It is important to note that some beers also need to be stored upright to ensure any live sediment stays at the bottom of the bottle.
Every beer has a shelf life. Beer will certainly "last" longer if refrigerated. That is, the flavor will evolve more slowly over time at lower temperatures. Storage at higher than room temperature will invite a turning of the beer's flavor for the worse.
In some cases, an aged beer might be considered to have an appealing taste, but still refrigeration will slow the aging process and allow the beer to be kept longer. Additionally, the flavor of highly hopped beers will degrade fairly quickly (within several months) at room temperature, and most people would agree that very hoppy beers in particular should be refrigerated because of this.
