You can pull up the site for everything Online Indexes and Lists. Most passenger lists are also indexed and available on the Internet.
One-Step Webpages Ellis Island, Castle Garden, and Other Ports 1820 - 1957 Ancestry.com ($) Immigration and Travel 1500s - 1957 Customs Passenger Lists, 1820 to 1902. These are lists that were submitted by the masters of ships to U.S. customs officials upon arrival in the United States. Customs passenger lists include each immigrant's name, age, gender, occupation, country of origin, and country or place of intended destination.
Immigration Passenger Lists, since 1883. These lists, also known as “ship manifests,” were submitted by the masters of ships to the Immigration and Naturalization Service and its predecessors. In addition to the same information found in the customs passenger lists, you may find the exact birthplace or last residence, marital status, previous U.S. residence, place of destination, and the names of relatives in the “old country” and in the United States.
The National Archives has the customs and immigration passenger lists and indexes from 1820 to the 1950s. These are described in Guide to Genealogical Research in the National Archives of the United States. You can request a search of the records at the National Archives with Passenger Arrival List form NATF 81.