FOREX-Dollar falls on worries over possible U.S. government shutdown

* Bit to keep US govt open stokes anti-dollar mood * Euro hold below 3-year peak versus greenback * Evidence of reserve diversification drags on dollar (Updates market action, changes dateline, previous LONDON) By Richard Leong NEW YORK, Jan 18 (Reuters) - The U.S. dollar fell on Thursday as traders piled into the euro, yen, sterling and other major currencies amid concerns over a possible U.S. government shutdown as lawmakers struggled to cobble together a federal budget d