The Gemara in Masechet Shabbat (19) establishes that it is forbidden to set sail on a ship within three days of Shabbat, which is understood to mean from Thursday. Even though the entire crew is not Jewish, it is forbidden to board a ship for a voyage on Thursday or Friday. The Rif (Rabbi Yishak of Fez, Morocco, 1013-1103) and the Rambam (Rabbi Moshe Maimonides, Spain-Egypt, 1135-1204) explain the reason for this Halacha based upon the requirement of Oneg Shabbat – enjoying Shabbat. People generally cannot feel enjoyment while sailing on a ship, as they are tossed and jostled, feel dizzy, and smell the unpleasant smell of the ocean water. By the third day, however, voyagers generally grow accustomed to the conditions and no longer experience discomfort. Therefore, it is forbidden to set sail on Thursday or Friday, as one will still feel discomfort on Shabbat, but it is permissible to set sail on Wednesday or earlier during the week, as one will already feel comfortable by the time Shabbat begins. This Halacha, and the reason given by the Rif and Rambam, are codified in the Shulhan Aruch.
The question arises as to whether this Halacha applies to modern-day cruises. Boats today are constructed with stabilizers, and the crew is able to steer the ship without causing much discomfort to the passengers. A verse in Tehillim describes the experience of sea travel as "Yahugu Yanu’u Ka’shikor," which means that the passengers are tossed about and stagger like drunkards, which is clearly not the case today, when ships are far more stable and cruises are generally comfortable. Indeed, the Meiri (13th century) writes that even in his day, sea travel was more comfortable than in Talmudic times, and there is thus room to allow embarking on a sea voyage on Thursday or Friday, as the trip will not interfere with one’s enjoyment of Shabbat. It should also be noted that the Shulhan Aruch explicitly limits this prohibition to oceanic travel, while allowing embarking on a voyage in a river, where there is no discomfort.
Rav Yishak Yosef (son of Hacham Ovadia Yosef), in Yalkut Yosef, cites the Meiri’s ruling and writes that it can provide a basis to justify the practice of those who embark on a voyage on Thursday or Friday. In his view, one should not rely on the Meiri’s position, but it does provide some justification for those who are lenient in this regard. However, Rabbi Moshe Halevi (Israel, 1961-2001), in his work Menuhat Ahaba (vol. 1), rules that one may rely on the Meiri’s ruling. He writes that if the Meiri considered ships in his day more stable and comfortable than in Talmudic times, then certainly nowadays, some seven centuries later, sea travel is comfortable enough to allow embarking on a voyage on Thursday or Friday. According to Rabbi Moshe Halevi, then, it is entirely permissible to embark on a voyage on these days.
One might, however, question this rationale based on the simple, empirical fact that even today many people experience sea sickness, and it is indeed difficult to experience Oneg Shabbat early on in a voyage. Therefore, it is certainly proper to be stringent in this regard, and not join a cruise that embarks on Thursday or Friday. If, however, one already purchased tickets before realizing this Halachic issue, and the tickets are not refundable, he may, in light of the financial loss at stake, rely on the Meiri’s ruling and go on the cruise.
Summary: One should not go on a cruise that embarks on Thursday or Friday, though one who already purchased tickets for such a cruise may board the ship even though it leaves on Thursday or Friday.