EUR has seen precipitous fall against USD in the past 1 year, from the levels of 1.47 in early 2011 to 1.24 in May 2012,due to weakening Euro Zone situation.
In the past 5 years EUR has seen the lowest closing level of 1.19 as on 8th June 2010. A fall below this level would see further downside for the EUR currency.
However it seems that most of the negatives in the Euro Zone is already priced into the currency. In case Greece exits from the Euro Zone, a fall below the levels of 1.19 cannot be ruled out.