Why is high fructose corn syrup unhealthy?
Besides a lot of propaganda there is not much evidence that high fructose corn syrup (HFCS) is more dangerous than normal sugar. Lets have a look at the sugar in detail:

HFCS is produced from corn and is originally a glucose syrup. Since fructose is obviously much sweeter, the glucose is converted enzymatically into fructose (see here for more details). Before the use in food production additional glucose is added to the syrup so that typical syrups contain 55% fructose and 42% glucose or 42% fructose and 53% glucose (the remaining % are water).

If you look at saccharose (which is our ordinary sugar) then this is a disaccherid which is build from one molecule of glucose and one molecule of fructose. The enzyme sucrase breaks this molecule up into one molecule of fructose and glucose each, so reaching a 50%:50% ratio between the sugars. 

As the ratios are more or less the same, it doesn't matter for the human body, where the sugar come from meaning that in this context it is more too much sugar in the food than a problem with HFCS, as also this study suggests: 


Straight talk about high-fructose corn syrup: what it is and what it
ain't.


Fructose itself is not without problems as this induces the production of fats in the liver, but again, it doesn't matter for the body, where this fructose comes from:


Fructose induced lipogenesis: from sugar to fat to insulin
resistance.


For further reading I can also recommend this article on Gizmodo: 


Is High Fructose Corn Syrup Really Bad for You?