Many US-based companies charge the same amount in the US as in Europe: a certain item will cost 100 USD when bought in the US, and 100 EUR when bought in Europe. This really means that the European customer pays 44% more for his stuff (1.44 USD = 1 EUR, today). Usually, this higher price includes the European Value Added Tax (VAT), which is around 20%. Still, American companies charge 24% more to European customers, presumably because the cost of selling for them is higher in Europe. Perhaps just because they can get away with it.
We are based in the UK and actually charge less in the US... Our pricing isn't too far from the exchange rate, but it isn't dictated by the exchange rate either. Pricing strategy should take into account the region you are selling into - the reason we are slightly cheaper in the US than we are in the UK is because the general market price for our goods is cheaper in the US. So we adjust our prices to remain competitive.
Look around at what your competitors are doing and if you are competing on price, then exchange rates are a low-priority influence on your pricing strategy.
Exchange rate hedging instruments are useful if you are trading lots of currencies to hedge against exchange rate movements. If a substantial amount of your revenue is coming in currencies other than USD, you are at risk from exchange rate movements. This isn't so much product pricing but how the company deals with cash management in multiple currencies.
Some markets and regions are more price sensitive than others and if you are charging more in those regions you need to be careful. That isn't to say you shouldn't do it. In Japan the prices for our goods are markedly more than the same goods in the US, but this is expected in Japan and the prices are still competitive. In China the prices are high (for good reason - import costs etc) as well, but there you have lots of grey importers who will look to purchase at the cheaper price in the US and then grey import into China where they can make a margin. In those instances it is in our interests to make it as difficult as possible for the Chinese customers to compare regional prices.