Just because the dollar is below the Euro does not mean the world (or America) is coming to an end. The dollar is not and has not been the strongest currency. The pound has been worth more than the dollar for longer than I can imagine.
The value of the dollar affects different aspects of business as well as the lives of Americans, especially those wishing to travel abroad. We must also remember the flipside: a strong Euro compared to the dollar makes European goods that much more expensive, and therefore that less attractive to American goods.
With America being one of the world's largest consumers of goods, the decline of the dollar versus the Euro also hurts European business.
Take this business case, although limited, as an example. An international airline is planning to purchase new aircaft. They have their eyes on the Boeing Dreamliner as well as the Airbus A380. From a purely cost effective standpoint, the Boeing would be more attractive due to value.
Of course the above example is extremely limited in scope, but I think the point is clear: the declining dollar in comparison to the Euro makes American goods more attractive to international buyers, which is something the domestic market needs.
China and Russia (throw in Brazil, India, Vietnam, etc.) are all considered Emerging Markets. Yes, their debts are low and cash reserves are high, but that money is going to go towards building up their respective country's infrastructure. Considering how much the US and US investors are vested in these countries, and their growth correlates to the growth of the United States economy.
If I was a celebrity or whatever and wanted a form of currency as an investment choice, why not choose the Rupee instead? It has more growth potential than the Euro.