Yeesh, I'm in New York now and I assure you *every* resident has a roommate. Relatively fewer are married (of the Americans at least), due largely to regional variation in marriage patterns. It's fun, actually; it makes residency more like a shared experience / prolonged youth than a soul-sucking job. It's nice to walk to work and back as well versus enduring a long drive home in commuter traffic.
Most people who move to New York do so because they are willing to pay a premium just to live here-- it's cramped, expensive and much less convenient than the rest of the country. You get by with little stuff, and you have roommates, and you spend most of your time out of your apartment exploring the city. But it's exciting and has an energy like no other place on earth.
Honestly, I think having someone to talk to and come home to (for the romantically unattached) is key in maintaining your sanity in any long-hours, demanding, high-stress job. Otherwise the loneliness becomes just too much.
And due to the high price of housing in New York (a very modest, very small 1-BR walkup costs at minimum $2000 a month) residency programs in Manhattan at the plusher hospitals do offer housing. Cornell almost requires their entire residency staff to live directly across the street from the hospital, and I've heard Manhattan Eye & Ear offers spectacular housing. Many others (like Columbia) have cut deals with private buildings to subsidize housing residents. The city hospitals however can't afford those sorts of perks, so (for example) Harlem residents (most of whom are natives of Africa and the Caribbean) live in the Bronx and have to take the subway into the city each day.
Regardless, however, the NY housing market is tight and does require significant security deposits, guarantees of income, and often a guarantor if you're young and haven't worked before. It moves quite quickly so be prepared to bring all of your financial documents with you when looking at apartments, to apply and to pay the deposit on the spot.
/lsres, congrats on your match!