The Rosh (Berachot, ch. 9, § 3) writes that the custom in Ashkenazic lands was to not recite Birkat Hagomel when traveling between different locales, unless the travels include passing through the wilderness with wild animals. On the other hand, he says that the custom is Spain was to recite the blessing on any trip because travel is inherently dangerous. He concludes that if one travels the distance of a Parsa, or 72 minutes, one should recite Hagomel, and if one travelled an especially dangerous journey of even less than a Parsa, one should recite the blessing. The Shulhan Aruch (Orah Haim 219:7) quotes the Rosh almost verbatim and gives both the Ashkenazic and Sephardic customs.
Rabbi Ovadia Yosef (Yabia Omer, vol I, Orah Haim, § 13), Rabbi Yehoshua Maman (Emek Yehosha, vol. I, 41 ), Rabbi Baruch Toledano (Kitzur Shulhan Aruch, pg. 256) and others write that Birkat Hagomel should be recited on any journey that is at least 72 minutes in length, even if it is one’s daily commute to work. This position appears questionable, because the dangers mentioned by the Rosh included wild animals and bandits, which are hardly threats nowadays. Although there are hazards involved with driving, such as accidents, it is unclear if the blessing was instituted specifically for animals and bandits, or any possible danger. Indeed, Rabbi Ben Zion Abba Shaul (Or LeZion, ch. 13, § 43) writes that the blessing was not intended for the collisions and the like, and only applies to travel where there is a high risk of bandits or pirates attacking the driver. When asked about the Sephardic custom, Rabbi Yosef Shalom Elyashiv also stated that one should not recite Hagomel if there are no wild animals or bandits. It should be noted that either opinion is halachically legitimate.
Regarding airplanes, even many Ashkenazic opinions say is to recite Birkat Hagomel because it is comparable to a boat, and a sea travel is one of the four main classes of situations warranting this blessing. Although airplanes do not travel in the sea, they are compared to boats because both modes do not travel on land. Indeed, Rabbi Moshe Feinstein (Igrot Moshe, vol. II, Orah Haim, § 59) says that any flight warrants the blessing of Hagomel. Others say that nowadays, air travel is very safe and the risk of accidents, hijackings, etc. is very low and thus no blessing should be recited. Nevertheless, the rule of thumb is that if one flies across an ocean then one should recite Hagomel, and if one travels between two close cities, then one should follow one’s custom regarding driving.
Summary: Depending on one’s custom one may or may not recite Birkat Hagomel traveling by car for more than 72 minutes. One should recite Birkat Hagomel on long–haul flights, but some are lenient with regards to short flights.