I'm going to NYC in March and have just been informed by Lufthansa that although I am flying in to JFK my return flight is now leaving from Newark, I had it all planned for how to get to and from Kennedy so I have been also looking up how to get from Manhattan to Newark.
The more expensive way of doing it is of course a Taxi or even a Limo.
A cheaper way is to take the Air Train(monorail)from your terminal to the New York Liberty Airport Station and then catch the New Jersey Transit train to Penn Station New York, from there depending on where in Manhattan you are staying you can walk, get a cab or take the subway to your hotel. The cheapest way seems to be by bus, take the no. 37 bus from the terminal to Newark Airport North Area then get the no.107 bus to the Port Authority bus station and then cab or subway to your hotel.
I got this info from the Trip Advisor site where there is a lot of info on ways of getting to and from Newark, I'm going to try the train.
I guess a lot depends on how much luggage you are carrying and whether you want to have to change busses and/or trains rather than get a taxi from door to door, especially if you have just had a long journey. I'm only travelling with hand luggage so hopefully it will be reasonably easy.
http://www.tripadvisor.com

There are also numerous hotels- airport shuttle services at reasonable rates. Much less hassle than going by train/subway/bus. These are shared van rides. Have a look at http://www.Supershuttle.com

I did not mention Super Shuttle because of the bad reports on Trip Advisor, they have one topic entitled Do Not Use Super Shuttle. I expect that many people have used Supershuttle without any problems but the consensus of opinion on TA site is that the service is poor, depending on where you are staying you can be riding round for quite a long time if your hotel isn't one of the first drop offs. .

Oh Okay, well take them off your list.... I have used them many times without problem,but there are many shuttle services available. It's just an option. To me the effort and carrying of luggage etc (most people will have suitcases) would rule out the train/subway choice. If in a group it's just as economical to get a cab. If solo then consider the shuttles.

I had origionally planned to use the shuttle service (I'm travelling solo) as I have done in many other major cities but was put off by the poor reports on Trip Advisor and a NY friend had said take the train as it will probably be quicker. I did say that I expected that many people had used the Shuttle without having a problem which you have just concurred with, so I may yet ride in a van from the airport.

We caught a cab up arrival at Newark to take us into Manhattan. You go to a booth across the road from the arrivals door and all fares are fixed.
Coming back we booked a car via Carmel limo and very very impressed with the service. Again they have set fares.

We booked online with nationwidelimo, they called to to confirm the reservation and were prompt, courteous (we were met inside the arrivals hall of Newark airport) and not too expensive, they will quote you a rate online and stick to it, you can pay the driver either by cash or cerdit card. On the way back to Newark we used them again and funnily enough got the same driver, he was a real laugh with all sorts of tips and hints and not to mention, great conversation..just what we wanted.

Looks like we'll be booking a cab. Thanks everybody.