Tonight's extract brewing had us waiting 30 minutes to get down to a reasonable temp. What did we lose in the process?
Relax, don't worry
Firstly, thirty minutes is not a long time. It's not particularly quick, but you're probably fine. Secondly, some pioneering Australian brewers developed a no-chill brewing method. Google it up.
Proteins coagulate during the cooling process. Because the coagulated particles of protein are heavier than the proteins themselves, they fall out of solution in the kettle or fermenter. Good cold break begets clearer beer. There may be small flavor impacts but probably not noticeable in beer.
Dimethyl sulfide (DMS) is an organic sulfur compound. In most beers it is present above its flavor threshold. It has a characteristic taste and aroma of cooked corn or creamed corn.
DMS precursors are found in malt and is formed by heating them above 160ºF. In the boil DMS is created, but easily driven off by the roiling boil. (This is one reason why you shouldn't boil with the cover on.) At flameout production continues until the temperature drops below 160º. The longer the wort is in this range, the more DMS you get in your fermenter.
In the fermenter, the evolution of CO2 scrubs DMS. Despite all its volatility small amounts (10-150 parts per billion) are perceptible in beer. It is better to reduce this off flavor and rapidly chilling your wort is an important step.
Cooling your wort quickly causes cold break material to precipitate out of solution. It can then be left behind in the brew pot or easily strained when transferring your cooled wort to your fermenter. If you cool slowly, cold break does not occur and the proteins remain in solution. The end result is cosmetic - your beer may suffer from chill haze. That is, it will be crystal clear at room temperature, but the proteins will precipitate slightly when cooled to serving temperature, but not enough to fall to the bottom, causing your beer to appear cloudy when cooled.
In addition to the main items (30 minutes isn't that long, cold break, DMS) listed by others, I'll add two other notes:
Infection: while the boil will sanitize the wort itself, if you leave the wort open to the environment while cooling, you can get airborne bacteria into your sweet sweet liquor and at a nice warm range of temps that will promote growth.
Hop utilization: Isomerization occurs below 100°C, though it does fall off by half pretty quickly. Depending on just how slow your cooling rate is, this might be a concern, changing your hop profile, especially for late additions.