Sometime in the 19th century, pneumatic tubes were constructed under Manhattan for the delivery of mail. They were sealed tubes that were installed mostly through existing underground infrastructure such as sewers and steam tunnels. Letters and small packages, pushed along by forced air moving at 35 mph, ran to and from post offices and, where traffic (and expensive fees) justified it, to offices in high-rise buildings in the financial district. These were used up until 1935, after which a couple of post offices moved, and a couple of new ones had been constructed, and it just wasn't worth anybody's time and money to extend the system. Mail is now distributed via more conventional methods.
The Urban Legend:
These tubes still exist underground, and various shifts and ruptures have opened connections to them from the sewers, steam tunnels, etc. in which they were originally built. In the course of remodeling, several unscrupulous architects have taken advantage of these abandoned tubes as drains through which rain can be diverted into the infrastructure below where it will be "somebody else's problem" and the upper ends now open in gutters and on slopes many stories high in the buildings that were once served with pneumatic mail. But, because the buildings are heated, these long stretches of the tube that run up through the building are held at temperatures much warmer than the outside air resulting, on cold winter days, in a powerful draft from those places deep in the earth that comes whistling out of these tubes at high speed. And every so often, a hapless cat, hunting rats deep in the underground, wanders too close to one of the air intakes and gets sucked up, through a twisting, turning, terrifying maze of tubing that batters the poor beast until finally it is launched, terrified, yowling, and often injured, out into the void thirty stories above ground. In certain offices these creatures are occasionally heard as they are launched nearby; in certain apartments which happen to be situated downrange, a cat, sometimes badly injured, occasionally lands on the balcony and, as soon as it recovers its consciousness and/or composure, demands to be let in. In other places cats are not so lucky and there is nowhere to land....
The Truth:
The guy who built this system back in eighteen-seventy-whatever, for reasons unknown, chose to test its suitability for 'fragile' packages by sending a cat, in a box, between stations to see whether it arrived at the destination with injuries. Why he chose this bizarre method of testing, as opposed to getting a bunch of tableware - plates, cups, glasses, etc - from a thrift store is unknown, and has led to some speculation about whether he just personally hated that particular cat. But ever since then people have been talking about cats getting into the tubes and 'accidentally' delivered to one of the destination stations. "High rise" buildings, in the context of eighteen-seventy-whatever, were no more than seven stories tall, and anyway the pneumatic delivery systems were all situated on the ground floor.