A nice, straightforward site called TheShipsList is worth a visit.
The name tells it all: this is a collection of ship passenger lists arriving largely in the US, Canada and Australia in the 19th century. You can conduct a quick search on a family name, or a particular individual, to see if perhaps it's included in the database here.
It's a bit hard to get a handle on the overall scope of things at the site. I'd guess there are at least a few hundred thousand passenger names included in the files here. Most of the passengers are European, from the looks of things. Not a huge collection, from a family history point of view, but a nicely focused specialty source of genealogical information.
The Cunard ship, Campania
There are also some excellent materials here on the ships themselves, along with descriptions, and a good FAQs section, on what it was like to actually travel as an immigrant...details on ticketing, steerage, naming conventions, record keeping, passports, and so on.
Well worth a look.
Visit the main page of Free Genealogy Tools for more, umm, free genealogical tools.
And don't forget to also check for your family history at Ancestry.com and NewspaperArchive.com.These are subscription databases, but they are among the most powerful research tools available for looking into family roots.