Rent in New York isn't as straightforward as it may seem due to price controls instituted in the 1940s that were initially designed to protect the wives of servicemen from being gauged while their male family members were at war. But let's step back for a moment briefly to discuss how (multifamily) real estate works in Manhattan.

There are three types of apartments you can buy and three types of apartments you can rent, but all of their occupants go through different silos in order to acquire possession via contract.

The three types you can purchase are:

1. Cooperatives: Cooperative buildings are the oldest form of multifamily housing in New York. Invented in the late 19th century, they were initially called "French Flats" in order to connote visions of Paris, where the upper and upper middle classes had been living vertically since the 17th century. Cooperative apartments require a purchaser to put down a deposit and then submit their financials (tax returns, a list of liquid and illiquid assets, etc.) for review by a board of neighbors (ergo the "cooperative" concept) who will then vote on the prospective purchaser's ability to live in that building. Boards typically demand a certain ratio of liquid net worth to purchase price: some buildings are 100% cash and supposedly up to 10x the purchase price in liquid assets (i.e. $1,000,000 purchase price requires $10,000,000 in cash and securities), while other more humble buildings simply want to see that you won't fall into foreclosure. Cooperatives are notorious for being immune from many standard practices in housing law due to their technical status as a corporation: cooperative owners are theoretical shareholders in a corporation that entitle you to live in the apartment you buy rather than owning the straightforward asset outright. The cooperative board of directors ("coop board") has the ability to deny the purchase or sale of any unit in their building for any reason whatsoever (race, class, ethnic status, religion) and do not need to disclose their reasons. Lots of the fancy buildings in Manhattan are widely known as either "Jewish" or "Christian" buildings, which once famously led millionaire Donald Rynne to opine "You must protect our building. Keep it Christian." in a 1997 board meeting at 740 Park Avenue. Approximately 80% of the buildings in New York City are cooperatives.
2. Condominiums: Condominiums are your standard purchase-sale freehold agreement where you own the bricks and mortar in your apartment outright. This is effectively a vertical simplex house. You must also pay property tax on your apartment (in cooperatives, property tax is levied on the corporation rather than the owner directly) in addition to common charges to keep the building afloat. Condominiums are the popular type of apartment in New York City since at 1988 when new-build cooperatives began to die off due to onerous ownership requirements, a lack of desire to reveal assets to strangers and, finally, the ability to rent your apartment (typically for 12 months minimum) and use it as an income generating asset in your absence. The number of pure condominium buildings in Manhattan has skyrocketed in recent years, but as a citywide asset class they sit at about a quarter of all multifamily units with the number of condominium units increasing on an annual basis.
3. Condops: Condops are a Frankenstein-like device used to divide an asset without going through the hassle of creating an expensive offering plan as required by New York State law. This allows a building owner to easily parcel out units above into residential units for sale while keeping possession of the retail or mixed-use space below. Condops are almost always leasehold deals, which means that the residential apartments above will revert to the landlord after a certain period of time -- typically 50 or 100 year terms, but leasehold apartments in London start at 100 years and go up to 999 years in length. The famous Guinness Brewery in Dublin was signed on a 9,000 year lease, but that lease has now lapsed due to the purchase of Sir Mark Rainsford's estate sometime prior to the First World War.

Most multi-family rentals follow an equally quirky track that has evolved over time, but they too fall into three broad categories:

1. Rent Controlled: Rent controlled apartments are the stuff of fantasy for most modern New Yorkers. They are unspeakably cheap and subject to a minute increase in rent that sometimes even fails to keep up with inflation. First introduced in 1943 when most apartments in New York were rental units -- including those vast spreads on Park and Fifth Avenue -- they are now relatively rare with approximately 25,000 units left and decreasing every year. The rule governing rent controlled apartments is that they must belong to a Tenant or the heir to a Tenant who has had possession to that apartment since at least 1971. Whatever the rent is on that date is the rent that will continue to be paid with extremely minor increases. The reason why Landlords hate rent controlled units is because they can rapidly force a building from a going concern to a completely unprofitable enterprise; one of many significant factors that almost destroyed the city in the 1960s and 1970s when "The Bronx is Burning." To give you an idea of how precisely cheap some of these units can be, I know one woman who lives across the hall from my mother that got her lease as a newly wed in 1938. She has a vast four bedroom apartment with maid's rooms that only costs her $300 per month. There are cases of even cheaper apartments going for $50 a month or less in prime neighborhoods such as Soho and the West Village that would otherwise rent at $4,000 to $5,000 per month if deregulated. A caveat: if you make over $200,000 per year, you are automatically disqualified from rent control and must deregulate your apartment immediately.
2. Rent Stabilized: There are over a million rent stabilized apartments in New York and some of them continue to be built today. Initially billed as a compromise plan between rent control and the free market, rent stabilized apartments tend to come on the market relatively infrequently. Having said that, virtually every building built between 1945 and 1971 is rent controlled so you have a lot of choice. Rent stabilized apartments are often acceptable to landlords due to the fact that they can derive large tax credits and abatements from their existence. Smaller landlords who don't have the capital to renovate or otherwise flip a prime asset are protected under this program.
3. Free Market: Pure, raw, unadulterated capitalism. You might even get a marble kitchen island.

The characters in Rent lived in a combination of rent stabilized and rent controlled apartments in what I believe was actually Alphabet City, which has a somewhat grittier vibe to the rest of the East Village. A mnemonic I remember hearing as a kid was always:

Avenue A? You're okay. / Avenue B? You'd better be brave. / Avenue C? You must be crazy. / Avenue D? You're dead.

This was not hyperbole. This is a picture of Avenue C in 1980. Some of the neighborhood was the occupied by squatters, but some simply lived in cheap rent controlled and stabilized housing dating back to the 1943 control board. Occupants of controlled apartments paid somewhere between $30 to $40 per month with super apartments going for up to $50 per month. (source) Those unfortunate enough to come after de-control could expect to pay about $250 while a peer apartment on the Upper East Side could fetch about $700 to $1000 a month according to this list of ads dating from 1982. Prices on the Upper West Side typically traded about 15% lower.