What is your definition of remote? If your definition is a location with more than a 30 minute drive to a Starbucks, then yes, there are some remote places in the Pine Barrens, the Kittatinny Mountains, and the Ramapo Mountains. If your definition is literally miles from a paved road, then there are
some locations in the Pines that will fill the bill, but other than that, this is a state of nine million people crammed between two major East Coast cities in the center of the Boston-Washington Metropolis. There just aren't many "remote" locations. Out of the way? Sure, but here in the Northeast, you're not going to get anywhere remote until you travel to the Great North Woods areas of New England.
All of that said, there are plenty of "out of the way" places in the Pine Barrens where not many people go simply because they are difficult to access because of bad roads, or a lack of roads altogether. For example, this photo:
Was taken somewhere around here in Bass River State Forest:
http://goo.gl/maps/xZZTI
It's a road going up a small hill about 110' high between Allen Road and Martha Road, both of which are unpaved. Allen and Martha are fairly wide roads and can be easily traveled in vehicles with a reasonable amount of ground clearance. Four wheel drive is helpful but not necessary. Allen Road is in bad shape and makes for a rough ride, but it's passable. Martha is in much better shape, but can be treacherous after a good rain. This unnamed road however, is a remnant, not frequently traveled, and as a result, four wheel drive is a requirement. Also, as you can see from the photo, the road is very narrow-barely wide enough for my compact Toyota pickup to fit through. The branches of bushes and trees on either side were scraping along the side of the truck and pulling at the mirrors and antenna. I don't mind because it's my firewood hauler/off roader/camping truck, but you wouldn't want to take your daily driver down this road if you care at all about your paint job. However, despite the "remoteness" of this area, it is only a mere 3 miles from the nearest major paved road (CR 653) and maybe would take 15 minutes to drive to provided you had the right vehicle and knew where you were going.
I wasn't sure where you were looking for a place to live, a place to camp, or as the other poster said, a place to bury something
but since you're looking for a place to live that's remote in NJ, my advice would be to look in and around the state parks and forests down that way. Most state parks and forests were started with one big land purchase, but eventually in fits and starts the state purchased land on the periphery, and ended up surrounding some pieces of property entirely. If you look at the map view of Google Maps at state parks, the "holes" in the green space generally means private land that is surrounded either by state park, state forest, or WMA property. IMO, that's the best of both worlds because you get to live in a remote place without having to own and pay taxes on the land around you, plus you know that it will never be developed. I know you're looking at the Pine Barrens, but there are a lot of folks in Northwest Jersey in this situation. There's a nice cluster of homes around a lake in Stokes that are completely surrounded by the forest. Then there are the folks who live in Walpack up in the Water Gap. Living up on the Kittatinny Ridge is is probably about as remote as remote gets for residential property in NJ.