New York is a new city, relatively speaking. In cities like Rome, Naples, and Paris the underground world is enormous - centuries (if not millennia) old quarries, ossuaries, and aqueducts catacomb huge sections of the underground. Archaeologists and underground societies spend years documenting these abandoned worlds, and are constantly discovering new offshoots and networks.
The underground world in the cities of the western hemisphere is mostly very different. There are a few unused nooks and crannies underneath New York, but for the most part anything underground is going to be part of the currently-in-use infrastructure of the city. Somewhere in between these two worlds lie the abandoned and never-used stations of the New York City subway system.
The most famous of these is the gorgeous City Hall station, built in 1904 and abandoned a little over 41 years later. This is also the easiest abandoned station to see - simply stay on the #6 train after the last stop downtown, and the train will loop through the station. If you actually want to set foot in the station, they open it up sporadically (I got to go during the 100th anniversary of the subway in October of 2004), and the transit museum gives tours a few times a year as well.
The other abandoned stations are different. Unless you're considering a career as a track worker, the easiest way to see those is simply to step off the edge of the platform and walk.
I could say I do or don't recommend the hobby of walking subway tracks, but it really would make no difference. It's like B.A.S.E. jumping, or apotemnophilia, or preaching on a street corner. Very few people feel the need to do it; those that don't aren't going to start, and those that do aren't going to swayed by someone pointing out why they shouldn't. Still, I will list some quick pros and cons.
Pros are in pretty short supply. In fact, unless you're the kind of person that's really into graffiti, graffiti history, urban infrastructure, and/or going places most people don't get to see, there really aren't any. The only one I can think of is the chance to experience a particular urban juxtaposition that I find really interesting - walking subway tracks and riding over them in a train are two almost opposite experiences in almost the exact same point in space. Riding is bright, crowded, noisy, and (relatively) clean. You're probably fairly relaxed. Walking is dark, solitary, quiet, and absolutely filthy. And you're probably very, very far from relaxed.
Now I do know people that have been walking subway tracks for decades and are as comfortable down there as they are in their own bedroom. Not me though. I've walked tracks on seven different subway systems on three continents, and I get the same slightly nauseated feeling of nervousness, the same adrenaline-fueled alertness, every time. I welcome it. In my book, subway tracks are no place to get comfortable.
Cons, as you might imagine, are much more prevalent. First and foremost, there is a very real danger of dying. It's not that large, but it's definitely there. People - sometimes experienced people, and sometimes even professionals - have touched the third rail or gotten hit by a train while walking tracks, both of which result in a very large dose of instant death. Other cons include the fact that you might get caught (generally not so bad unless you have graffiti paraphernalia on you), and the aforementioned dirt and darkness.
Still, these cons haven't kept me from visiting most of the abandoned stations and platforms that dot the tunnels of the New York City subway system. Generally these visits are fairly chill affairs - time the trains, make sure nobody's looking at you on the platform, and off you go. One time, however, was different.
It was a while ago, when I was fairly inexperienced and still didn't quite know what I was doing. Our goal was one of the abandoned IRT stations in Manhattan. It started out pretty well - a train passed and we were off. We stuck close to the wall, on the opposite side of the tracks from the third rail, walking at a brisk but controlled pace. But before we reached the platform another train passed coming the opposite way. There was nowhere easy to hide and we hit the abandoned station in a panic, sure we had been seen and reported.
I wanted to go back to the local station, which is where we came from, but as we were closer to the express station my companion thought it better to try to get out there. Big mistake. There was a reason we had used the local station instead of the express - express stations are really busy, and as we approached it seemed certain we’d be seen coming out of the tunnel. We ended up hiding in a little nook between the express tracks, about 100 feet from the station, contemplating our next move.
We didn't get to contemplate for long - flashlights were coming our way from the station. “Run!” my companion said. This was a lot different from the careful excursion coming in. The “brisk but controlled” pace went out the window. We booked it down the tracks, constantly hopping the third rail while having to dodge the other trains that came along.
We got back to the local station and jumped back up on the platform. One guy dressed in civilian clothes was staring right at us as we exited. We were sure he was an undercover cop. But we couldn't very well head back onto the tracks, so we did the only other thing we could - pretended like we belonged there, and walked confidently toward him.
Still, I was sweating bullets as we came up to the guy, ready to have him whip out a pair of handcuffs at any moment. But as we came closer we noticed he was dressed pretty shabbily, even for an undercover cop - it was obviously just a guy hoping to bed down for the night in an out-of-the-way corner on a not-so-busy platform. “Oh thank God man,” he said, as we passed him, “I was sure you guys were cops.” We gave him a quick smile and got the hell out of there.
More about the abandoned subway station of New York City can be found here