The Shulhan Aruch (Orah Haim 219:9) records a dispute regarding whether or not Birkat Hagomel is to be recited after dangerous situations, other than the four mentioned in Tehillim (one who was ill, one who traveled in the sea, onewho crossed the desert and one who was in prison). In this context, a dangerous situation involves one where there was a real possibility of loss of life (h’v) or serious injury. For example, being nearly hit by a car is not what is being to referred to here by the Shulhan Aruch. On the other, actually being hit by a car and surviving is more in line with the Poskim’s definition of otherdangerous situations. Rabbi David Abudraham (Hilchot Berachot, Sha’ar Shemini) says that Birkat Hagomel was instituted only for the four specific situations and therefore one would not recite the blessing after other miraculous events. On the other hand, Rabbi Itzhak Barsheshat (Shu”t HaRivash 337) says that the Gemara explains that the blessing is recited on those four situations because they are understood to be very dangerous, but that it is not an exhaustive list. The Ben Ish Hai (Parashat Ekev) says that these four miracles could easily be mistakenly attributed to nature and thus they were included in the blessing to show that they were from Hashem, but not to the exclusion of other situations.
The Shulhan Aruch concludes that since it is a dispute, one should recite BirkatHagomel without Hashem’s Name. Rabbi Avraham Azoulay (Gloss to Levush, § 219), the HIDA (Mahazik Beracha & Haim Sha’al, vol. II, § 15), the Bet Oved(pg. 104, § 13) all concur. Rabbi Shalom Messas (Shemesh Umagen, vol. III, § 63) and Rabbi Yehuda Ayash (Bet Yehuda, § 6) write that Birkat Hagomel with Hashem’s Name should be recited anytime one came out of a dangeroussituation. It should be noted that generally speaking the Ashkenazic approach is to also recite Birkat Hagomel for an dangerous situation. Nevertheless, it appears that the mainstream Sephardic custom is to follow the Shulhan Aruch’s opinion.
Summary: One should recite Birkat Hagomel without Hashem’s Nameafter dangerous events other than the four enumerated in Tehillim and the Gemara.