Well, I know where I'm heading first the next time I'm in Hamburg. More than 5 million Europeans (including several of my ancestors) left for the New World via the port of Hamburg between 1850 and 1934, and now -- thanks to a new museum -- you can get a sense of what it was like for them -- just as you can at Ellis Island in the U.S. or the Cobh Heritage Centre in Ireland.
Museum where past masses huddled
If you want to do some digging to see if your ancestors might have spent some time there, you can explore the databases at Ancestry.com:
Hamburg Passenger Lists, 1850-1934
Hamburg Passenger Lists, Handwritten Indexes, 1855-1934
And to learn a little more about the museum and port itself, you might want to poke around this site: Ballinstadt