An air stone is a better idea because it diffuses the force of the air bubbles. When you don't use one the bubbles that come out of the airline are huge and come up powerfully, taking considerable amounts of water up with them. This current that it creates is not only too strong, but since it is so unsteady it really knocks things around in the tank. Not something you want.
Plus it is believed that finer, more numerous bubbles make gas exchange easier.
There are only a handful of scenarios when I would use, or advise using artificial aeration:
* In a tank that has a very tight-fitting lid, where little new air is getting to the water surface for gas exchange. This only applies when there is an internal, canister or no filter, as a power filter would be providing plenty of exchange just through its normal running mechanism. (When I had an Eclipse Corner 5 I didn't like the idea that the whole filter was encased in this sealed package of a hood, so even though it was a bio-wheel, it was still being smothered in a way. In that case I actually ran just an airline under the hood, but not actually under the water. It was only to introduce a constant supply of fresh air to the water surface.)
* In a tank with current-loving fish that doesn't have a lot of current in its filtration system.
* At night in a heavily planted tank that is using CO2. When the lights go out, the plants start breathing oxygen instead of the CO2. This small addition of extra surface agitation and increased air circulation above the water is believed by some (Most notably Takashi Amano) to keep O2 levels elevated enough to lessen any stress on the fish who are competing with the plants for the O2.
Otherwise it's aesthetic; and it generally has some benefit in keeping the tank water a little fresher. If you like it, use it. But definitely use a stone, wand, pad or diffusor.