Passenger lists, also known as manifests, are a list of passengers who purchased tickets for the voyage. Many of our ancestors arrived by ship but some of the online databases will include airline manifests and other means of transportation across our borders.
Most of my experience is with arrivals into New York, specifically during the Ellis Island years. Whenever possible, I'll try to include links to websites that provide a more general overview of US immigration.
What passenger lists are online? See:
Access to some of the databases requires a subscription, like Ancestry.com. Others, like the Ellis Island Records database is free to search but if you want copies of the original ship manifests, you'll have to purchase them or learn the trick for saving them for free (can't just right mouse click). Databases are being updated on a regulars basis...thank goodness, I have yet to sit in front of a microfiche machine.
Another useful link is Finding Passenger Lists & Immigration Records 1820-1940s
arrivals at US ports from Europe at:
This website lays out resources for all major US ports for online databases, microfiche, CD, and books.