At one time or another, it seems that almost every family in America passed through New York City. Most typically, this was the major port for newly-arrived immigrants, passing through Ellis Island (and earlier, Castle Garden) on their way to Manhattan or the outer boroughs.
But even for US natives, New York held a special draw for those wishing to make it big, or simply to find work in one of the world's largest metropolitan centers.
To check on your own family history in New York, start with the New York City Death Index for 1891-1948. This massive list of almost three million death certificate records can be easily searched by last name on a full name search, a partial name (with wild card searching), or with a sounds-like surname. Searching can be fine tuned with first name, dates, or a choice of boroughs.
The NYC Death Index is provided courtesy of the Italian Genealogical Group, who also makes some other wonderful NYC and Long Island databases available, though none as large as the death index. You don't need to have Italian ancestors to find some very valuable family history information here. Visit their site to peruse their bride and groom records, births, marriages, and naturalization records. There are also databases linking Italian surnames to the particular towns in Italy from which they came.
NYC Ballplayer, Back in the Day
Don't forget to also check for your family history at Ancestry.com and NewspaperArchive.com. Yes, these are subscription databases, but they are also among the most powerful research tools available for looking into family roots.