I often get asked if there are any passenger lists in Rotterdam or Amsterdam, of the people who departed from these ports to America, Canada, or Australia. Depending on the period, there may not be any. Passenger lists often went with the ship and were archived in the port of arrival, not in the port of departure.
The archives of the shipping companies sometimes have passenger lists. For example, the Rotterdam City Archives have the archives of the Holland Amerika Lijn and its predecessors, which include many 20th century passenger lists. But many of these passenger lists are also available on Ancestry, like in the New York Passenger Lists database, so you may not need to come to Rotterdam to see them.
For the 1800s, it is rare to find passenger lists in Dutch archives. The archives of the Stoomvaart Maatschappij Nederland, kept at the Rotterdam City Archives, include lists of passengers to the Dutch East Indies. For the New Netherland period (1600s), I do not know of any passenger lists in Dutch archives.