If you have ancestors who entered the U.S. through New York between 1820 and 1892, take a look at CastleGarden.org. Castle Garden, the New York immigration port prior to the opening of Ellis Island in 1892, is easy to search. Here are a few hints:

• Try using the asterisk (*) as a wildcard when having trouble with variations in spelling; e.g., N* gets several versions of Nick, Nic, Nicholas, etc.  
• Once you find the name/ship/date of an ancestor, try searching that surname on the same ship and date to see if several members of a family traveled together.