The problem with this question is there are a great number of brewing substances that cause a hangover, including the fruit of the labor itself (ethanol). Anecdotally, having friends in the medical profession, I've had water added to my blood stream artificially after drinking. This of course predicatbly reduces the experienced hangover, but it does not completely cure it.
Moderation is always going to be the BEST cure. But not always the practical cure.
That being the case, from a drinker's perspective, we want to consume only the amount of ethanol to cause the desired effect and no more. We want to consume a sufficient amount of water (to dilute the after effect of ethanol) and vitamins--particularly B vitamins, to lessen the negative effects.
From a brewer's perspective the obvious is to limit the amount of ethanol. This isn't always desirable as it also limits some of the perceived benefits of drinking. To make drinkable "effective" beer we need to: lessen congeners (found commonly in dark alcohols but not necessarily dark beers), limit fusel alcohols, lessen the carbohydrate content of our beers and maintain an acceptable amount of electrolytes in our beer.
Reasons against limiting ethanol are obvious. Have you ever drank a low ABV beer? Not only does it taste bad, but it also does not cause any sort of pleasant inebriation.
1) Congeners are substances found in dark alcohols (dark rum and whiskey) and not in light alcohols (vodka and gin). The difference between the spirits is obviously the color. Other than that, dark alcohols are commonly aged in Oak barrels. Apparently that is hangover producing (I can't say why). They also tend to have a higher sugar content, which is probably an additive to hangovers. The lesson is to limit free (unfermented) sugar in your brew.
2) Fusel alcohols, along with the "heads" of fermentation are the non-desirable types of alcohol other than ethanol. Many types of alcohol exist (at least 18), the one we desire is known as ethanol. Readers may also be familiar with methanol and isopropol. These area both alcohols, but when metabolized have negative effects on a person. A discussion of the types of alcohol exists here: http://en.wikipedia.org/wiki/Alcohol. A brewer should aim to minimize the number of fusel alcohols while producing ethanol. A key control to this is a careful watch of fermentation temperatures. Typically a cooler temperature is better, but each yeast strain has a preference.
3)Commercial yeast strains always have an average attenuation advertised with them. In overly simplified terms, this number represents the amount of fermentable sugars that are actually converted to alcohol. The higher the number, the lower sugar content in the final brew. This will obviously have drastic effect on the final brew of the beer if the intent is something sweet. Still, the higher the carbohydrate (read sugar) content of the final brew, the greater the hangover effects.
4) Adding electrolytes, known more commonly as salts, may help the consumer. I don't known of anyone in the brewing community who presently does this, but there are theoretical beers which are hydrating by themselves. http://www.giantfreakinrobot.com/scifi/scientists-create-beer-hydrates-drink-alcoholics-rejoice.html. I have yet to see one of these, but I would love to see the homebrewing community create one!