The Staten Island Ferry runs across New York Harbor between Whitehall Street (next to Battery Park in Lower Manhattan) and St. George terminal in Staten Island. The free 25-minute ride gives you a view of the Financial District skyscrapers, the Statue of Liberty, and Ellis Island.
New York Water Taxi shuttles passengers to the city's many waterfront attractions between the Hudson River (on Manhattan's west side) and the East River (on its east side), including stops in Lower Manhattan (for access to the 9/11 Memorial Museum) and the South Street Seaport, as well as multiple locations in Brooklyn.
An all-day pass on the water taxi is $37; a similar pass that also allows passengers to visit major attractions like the Empire State Building or 9/11 Memorial Museum as part of their sightseeing package starts at $59.
Also consider NY Waterway, which runs ferry service across the Hudson River between Manhattan and ports in New Jersey and upstate New York. In addition, the NYC Ferry operates along the East River, connecting Manhattan with Brooklyn, Queens, and, seasonally, with Governors Island (the ferries also connect several locations within Brooklyn and in Long Island City, Queens).
NY Waterway ferries offer single-trip ($9–$21.50) and monthly passes ($196–$642.50); the price varies greatly based on the the length of the trip. The NYC Ferry (operated by Hornblower) has one-way tickets for $2.75, or you can buy a 30-day pass for $121.