The Metropolitan Transportation Authority was created in 1968 to oversee public transportation in entire New York City area. Within the city, the subways and most buses are operated by the New York City Transit Authority.
This page covers only the streetcar and bus systems. The Subway system is well covered with the New York City Subway Resources Web site.
In New York City, they are known as depots. Certain depots are identified as serving one borough, but actually located in an adjacent borough.
Between 2004 and 2006, MTA formed a new subsidiary, MTA Bus, to take over the remaining private bus companies serving New York City. Those depots are also shown, most of them are still owned by the former private companies but now leased by MTA.
Brooklyn Manhattan Transit
The Bus Rosters Page
Metropolitan Transportation Authority (Wikipedia)
MTA Regional Bus Operations Bus Fleet (Wikipedia)