If your ancestors immigrated to the United States from Germany, they almost certainly traveled by boat. Even ancestors who came here from other European countries -- France, Russia, Italy, Sweden -- may well have left the continent from a German port.
In either case, here's an important resource worth checking. The German Emigrants Database (the elegant-sounding Deutsche Auswanderer Datenbank in German) is a joint project of German and American organizations, specifically:
- Castle Garden Immigration Research (New York)
- Historisches Museum (Bremerhaven)
- Förderkreis Historisches Museum (Bremerhaven)
Here's a direct link to the search form (though you may want to click through the site first for background info). You can search on surnames as well as gender and a range of dates. The data is mostly compiled from a large (and growing) collection of shipping manifests.
The German Emigrants Database includes other useful content: information on ships, research tools, and a collection of almost a century's worth of photographs covering the period from 1840-1938.
On a related note, the Staats Archiv in nearby Bremen also has searchable passenger lists for 1920-1939 (the page is in German, but there's a button for English at the top right of the page). I'm not clear on how much overlap (if any) there is with the Bremerhaven lists. If anyone knows, please post a comment.
Don't forget to also check for your family history at NewspaperArchive and Newspapers.com. These are subscription databases, but they are among the most powerful research tools available for looking into family roots. And visit the main page of Free Genealogy Tools for more, umm, free genealogical tools.