About forty percent of 19th century immigrants from Germany and Eastern Europe left through the city of Bremen. German ports typically kept records of emigrants leaving for America and elsewhere; unfortunately, the emigration lists from Bremen were destroyed during World War II. German Immigrants: Lists of Passengers Bound from Bremen to New York compiled by Gary J. Zimmerman attempts to reconstruct these lists.
Based on passenger lists of arrivals at New York, German Immigrants includes information on about 35,000 immigrants spanning the dates between 1847 and 1871. This is still only about twenty-five percent of the total number of emigrants from Bremen arriving during this period.
This series spans four volumes and includes details such as age, place of origin, date of arrival, and the name of the ship, as well as citations to the original source material.
German Immigrants is a good starting point for finding your German immigrant ancestors.