The American Family Immigration History Center made Ellis Island arrival records accessible online at http://www.ellisislandrecords.org/. The database covers arrivals from 1892 to 1924, the peak years of immigration. The ship manifests identify passengers by name, arrival date and nationality. (Due to the great number of visitors to the site, it is sometimes inaccessible. If you cannot connect, try again later.)
Read about the Ellis Island records site in this New York Times article (registration required) Family Tree Magazine offers some tips on how to access the site and make the most of your time there.
The official Ellis Island site explains the history and significance of the port of entry, as well as the genealogical research that can be done there. Search the Wall of Honor, which lists a limited number of immigrants. (Again, the site is inaccessible at times due to high traffic.)