Vodka's actually one of the best alcohol types you can have with regard to avoiding hangovers.
*Puts Diageo Scientist's Lab Coat on*
The hangover is caused by 2 things:
Dehydration - as Davie has very correctly mentioned
and
The level of Higher Alcohols in the Alcohol you were consuming.
Higher alcohols are compounds including Methanol, Acetaldehyde, 2/3 Methyl Butanol, Acetal, Ethyl Acetate etc, that are made through the distillation and maturation of a product.
Grape based products ie, Brandy, Cognac, Wine etc have a comparatively high level of Methanol due to the grape source. Tequila also falls into this higher Methanol level due to the Agave Cactus source.
Whisky contains generally little Methanol, but high levels of other higher alcohols. Acetaldehyde increases with age.
Vodka, however, is generally distilled from Grain or Sugar, which produce very low levels of Higher alcohols and methanol. It's then filtered through Charcoal that further removes impurities.
It's because of the metabolism of Methanol -> Formaldehyde (the stuff they used to use as a preservative for medical studies) and then to Formate that causes the headache.
Whereas Ethanol (the higher part of Vodka other than water) metabolises to Acetaldehyde and then Acetic Acid.
As a general rule: The darker the drink, the worse your hangover...
Also, the idea behind drinking strong Coffee to sober you up is that it speeds up your metabolism of Alcohol, so it leaves your system quicker.
My work here is done =P
M