Thanks to Steve, my Greek buddy, for an interesting story...his family arrived in NY in 1905. This reminded me that not everyone knows about Castle Garden and Ellis Island. From 1855-1890, Castle Garden was the point of immigration. From 1892-1924, Ellis Island was.
I'm providing the links here: http://www.castlegarden.org/ and http://www.ellisisland.org/. These are free services (no subscription).
I particularly like the timeline provided on the Ellis Island site:
If you know the ship, you can search the databases above, or also http://immigrantships.net/nycarrivals1_6.html
See also US Citizenship and Immigration Services for record copies: http://www.uscis.gov/portal/site/uscis/menuitem.eb1d4c2a3e5b9ac89243c6a7543f6d1a/?vgnextoid=d21f3711ca5ca110VgnVCM1000004718190aRCRD&vgnextchannel=d21f3711ca5ca110VgnVCM1000004718190aRCRD