Consider this resource, even if your ancestor was not German. The lists are complete for all passengers, not Germans only. The criteria they used in selecting was to only transcribe lists where at least one German was travelling.
The author cites that four million Germans arrived in the United States between 1847 and 1895. A really helpful piece of information is that German emigrants prior to the 1830's were "almost exclusively from Southwest Germany, Wüerttemberg, Baden, Bavaria, and the Rhineland-Palatinate."
Also keep in mind that emigrants did not always leave from their home country. Sometimes they traveled to another port before setting sail. On March 5, 1860, the SS P. Flood arrived in New Orleans from France. On board were travelers from Germany, France, Italy, and Switzerland.
Emigrant agents advertised travel to the United States. They earned their living by convincing people to move to the New World. Of course, they painted a more sophisticated and less hostile picture than many settlers encountered. But many emigrants did not pack their bags and set sail based solely on a whim. The emigrant agent was committed to doing a hard sell.
As a result, often an entire extended family or even an entire village would sail together with no intention of remaining in New Orleans.
So how do you research this? One of my favorite sources is The Ships List which has been online for almost a decade - a virtual lifetime on the worldwide web. This group has been busy, and you'll find a ton of information here, including definitions and explanations of terms and customs.
It has "Passenger Ship Arrivals for the Ports of New Orleans, LA and Galveston, TX - 1847" online, in addition to many other lists. This site offers a really nice Resource Page for researching emigrants.
Another source is the Immigrant Ships Transcribers Guild. What you'll quickly realize is there is a tremendous amount of information about the immigrant ships in existence. You'll also realize a lot of it is has been scanned, but may not easy to read or may not be searchable yet at all. You can even help out with this group by transcribing more ship lists.
Many immigrants traveled a much shorter route than did the Germans. According to "The Century," numerous refugees from St. Domingo had escaped to Cuba prior to the early 1800s. International friction between France and Spain forced them to flee again. During the sixty-day period between May and July 1908, nearly 5,800 emigrants arrived aboard 34 ships from Cuba. Among them were whites, free mulattoes, and black slaves. Eventually nearly 5,000 more arrived from Cuba, Guadeloupe, and other islands.
Ships lists will also show that some emigrants landed in Cuba, Puerto Rico, and other island locations before traveling on to the United States. Others, sailed to Canada, Philadelphia and other North American ports, before taking another ship to New Orleans. Sometimes it was more economical than sailing directly to New Orleans. If you don't find your ancestor in the logical ship lists, try some of these alternative routes.