http://en.wikipedia.org/wiki/Eschatology_of_Jehovah's_Witnesses#Presence_of_Jesus_Christ

Jehovah's Witnesses believe that 1914 is the start of the end times and is when Satan was cast out of heaven. They look at the book of Daniel and did some basic math to come up with 2,520 years. They then walk back 2,520 years from 1914 and come up with 607 B.C.E. The parts of Daniel they pick out talk about the destruction of Jerusalem. So, they claim that 607 was when Jerusalem was destroyed by the Babylonians. Except it wasn't, it was destroyed 587(or 586).

In an attempt to sure up their 607 date they take 70 years, which is the length of the exile, and count back from the year of the temples reconstruction and get 607. A major problem is that the date that historians believe the template was rebuilt is based on the 587(6) date. Jehovah's Witnesses then go on to claim that historians are wrong and the bible is right while continuing to cherry picking dates from the people they claim are wrong.

They also like to point at some minor issues with Canon of Ptolemy as proof that historians are wrong. They do this while ignoring that the Canon of Ptolemy is no longer the corner stone of the date they are attacking and that the date is now based on administrative tablets from that time.

Here is more specifics about the issue: http://carm.org/1914-ad-607-bc-586-bc-and-jehovahs-witnesses