Congeners are not
mysterious. They are simply
chemicals related to
ethanol which are produced in the
fermentation process. Fermentation happens when
yeasts eat
sugars and
excrete alcohols; however, not all these alcohols are the
ethyl alcohol that you want to drink.
Some congeners, such as methanol, are indeed quite nasty. Methanol, in sufficient quantities, can make you go blind or even kill you. In smaller quantities it will give you a rather nasty headache. It is from this effect that badly-produced, high-methanol moonshine was known during Prohibition as "popskull".
In general, dark liquors such as rum and whiskey contain greater congener content than clear ones such as vodka and gin. Red wine contains loads of the stuff, which is ironic because (when taken in moderation) red wine is good for you. I don't know, but I would guess that charcoal-filtered whiskeys (such as Jack Daniels), and triple-distilled Irish whiskey (such as Bushmills) would contain less congener than plain bourbon or Scotch whisky.
Congeners are partly responsible for hangovers, but they are by no means the only factor. The metabolism of alcohol tends to deplete your body of certain nutrients; eating more of these nutrients can reduce the chance of hangover. Vitamin B6, in horse doctor's doses, has been demonstrated to reduce hangover. Protein also helps. In addition, the hair of the dog may actually do some good, since a small quantity of ethanol may block the conversion of certain alcohol metabolites into formaldehyde.