There are roughly nine branches of NJ Transit train lines in the North and "Central" areas of New Jersey. This is not including the PATH system, the Hudson-Bergen Light Rail or the Newark Light Rail.
In South Jersey there is one, the Atlantic City Line. But there is also the River Line and the PATCO. . . which are kind of the southern equivalents of the PATH and Hudson-Bergen Light Rail.
The biggest reason why this passenger rail divide exists is purely population . . the center of the state's population (as of 2000) is in East Brunswick in Middlesex County. . . and that is why most of the rail lines are north of the pop. center (notice how the above map divides the state too).
But New Jersey used to have some older railroads. Check out this great website and see the progression of South Jersey's railroads. Then check out this North Jersey historic rail site (which could use some updating).
There are also some in Northwestern NJ that are still around for tourists today. Some that I have not mentioned are freight railroads - a pretty good list can be found here of all rail lines in New Jersey.
So the question is - if you could build a passenger rail line in New Jersey, possibly to make your work commute easier, (of course NOT keeping in mind our state's deficit) . . . where from and where to would you build it?