From 2000 to 2007 the USD lost half its value with respect to the Euro. Refer the Euro-USD chart below:
This is exactly as per theory. But in the short run when investors seek to avoid risk they move into safe assets. So currencies like US Dollar, Swiss Franc appreciate in value. Similarly Gold gains when investors seek safety over returns. So in the last 6 months the dollar strengthened against other currencies.
In many respects India and US are remarkably similar. India has a huge fiscal deficit and is a net importer of goods. Last year India's Trade Deficit was over $100bn which as a percentage of GDP is worse than America !! This trade deficit was financed by foreign investors who bought Indian stocks and bond by the truckload. So, the rupee remained stable, when the stock market declined, the inflows dwindled and the rupee weakened.
India does not have Capital Account Convertibility. The Reserve Bank of India's official is to prevent sudden volatile movements in the currency markets. The RBI does not try to fight the trend; it tries to smooth out the volatility.
There was an article in the New York Times weekend edition about the US Dollar. Read the article here