Based on various airlines you may consider to book very attractive direct flights between Europe and New York. The lowest fare available is based on current promotional offer of Norwegian using their 30% discount code and departing from Scandinavia, Berlin or London. However plenty of other interesting deals are available such as direct flights from Italy (Milan) already for €339 with Alitalia. Travellers in Italy may consider to departing from Berlin or Dusseldorf already for €365. (based on service of Air Berlin).
Travel options vary by each origin and airline but in general you may find the lowest fares during European winter 2015/2016. (look for flights departing till end of March 2016). Below you may find few suggestions if you are looking for straight way to New York as one of the most demanding destinations..
UK – New York from £220 (open jaw flights with British Airways)
Paris – New York from €397 (choose Skyscanner FR)
Booking sample of cheap direct flights from Europe to New York from €196! In this case you would be departing from Oslo to America on 31st of January 2016. Your return flight from New York back to Norway would be on 5th of February 2016. Remember that in case of flights with Norwegian only hand luggage is included in base fare..