HaGaon Rav Shlomo Zalman Auerbach zt”l (Halichos Shlomo, ch. 23) considers flying on an airplane a sakana (dangerous situation), and therefore one must always recite Birchas Hagomel after flying (even if the plane did not fly over an ocean or desert).
However, most poskim disagree with this opinion, as statistics now show that it is more dangerous to drive in a car than fly on an airplane. Using this line of reasoning, some poskim rule that one should never recite Birchas Hagomel after a plane trip, even if the plane flew over an ocean or desert. (HaRav Dovid Zucker, shlita, quoting HaGaon Rav Yaakov Kamenetsky zt”l).
HaGaon Rav Moshe Feinstein zt”l (Igros Moshe O.C. Volume 2 Siman 59) agrees with HaRav Shlomo Zalman Auerbach that one should always recite Birchas Hagomel after any plane trip. However, his reasoning is different than HaRav Shlomo Zalman Auer-bach’s. R’Moshe explains that just as Chazal require one who travels by sea to recite Birchas Hagomel, regardless of whether his trip was a sakana or not, so too, any traveling that is not done on secure, dry land, requires a Birchas Hagomel upon completing the journey.
Some poskim say that one should be machmir (strict), and taking all views into account, recite Birchas Hagomel without the sheim v’malchus (name of Hashem).
However, the most prevalent minhag is to recite Birchas Hagomel with the sheim u’malchus upon flying over an ocean or desert. If one did not fly over an ocean or desert, no beracha is recited at all. (Minchas Yitzchak Volume 2 Siman 47, HaRav Dovid Zucker, shlita, Harav Shmuel Fuerst, shlita).
According to HaGaon Rav Moshe Feinstein zt”l, one only recites Birchas Hagomel at the end of the return trip. For example, if one travels from Eretz Yisroel to Chicago for a short visit (less than 30 days), he does not recite Birchas Hagomel until he arrives back in Eretz Yisroel (Rivivos Efraim Volume 1 Siman 155). The only exception to this rule is if one travels from outside of Eretz Yisroel (ex. Chicago) to Eretz Yisroel. Then the hope is that Mashiach will come, and his trip will not be a temporary one. In this case, R’Moshe says that one should recite Birchas Hagomel in Eretz Yisroel, and then again upon arriving back in Chicago (HaRav Shmuel Fuerst, shlita).
If one travels by boat across the ocean or large sea, he should recite Birchas Hagomel at the end of his trip upon returning to dry land. However, if he travels through a river, no beracha is recited. (Note: This is according to Minhag Ashkenaz. With regard to Minhag Sefard, see Biur Halacha 219:1 “Yordei Hayam” and Piskei Te-shuva).
To become obligated in Birchas Hagomel, one must travel a considerable distance offshore. This can be relevant to people who go on cruises. Each cruise is different and a shailoh should be asked as to whether a Birchas Hagomel should be recited.