Should someone say the HaGomel blessing after taking an airplane flight? I seem to remember this being the practice, but honestly the average commercial airplane flight these days is 10 times safer than driving to the supermarket...
There are various Halachic opinions on this subject. This article by Rabbi Doniel Neustadt (pg. 3-4) sums up the various opinions very nicely (see footnotes there for names):
He then goes on to say that the general custom today follows #2 above.
I also saw that R' Moshe Feinstein zt"l held that one should only say Hagomel on the return trip (if the trip is less than 30 days). The exception to this is if one is traveling to visit Israel, where Ha-gomel should be said after both directions (i.e. after landing in Israel, and then after landing back in America). (taken from here pg. 2-3)
For a practical decision, please see a Rabbi.
The basic rule is to say hagomel after crossing an ocean (on water) or a desert (on land) but not after other trips.
http://www.mevaseret.org/mmy/searchshiurim.php?shiur=105 lists various rabbis' views regarding airplane travel. I haven't checked the sources it cites, but if it's to be trusted then Rabbi Sternbuch cites others as saying not to say it unless the flight was "eventful" [whatever that means], the Tzitz Eliezer says to say hagomel after any but a short domestic flight, and Rabbi Moshe Feinstein says to say it after any flight.
As always, for practical guidance, CYLOR.
Update: I've checked the sources of that Web page, but have skimmed them rather than read every word. (That's always dangerous, but) AFAICT the Tzitz Eliezer actually says to say hagomel after going over a desert or ocean [yam, which may include larger seas or what-have-you], unless it's a short domestic flight. I don't see that he says to say hagomel after a long flight that doesn't go over a yam or desert, which is what the Web page implies in his name. Rav Moshe Feinstein is quoted correctly AFAICT. Rav Moshe Sternbuch is quoted incompletely. He actually writes that the custom in South Africa is to say hagomel after any flight over the yam [or, I suppose, the desert?]; he also quotes the Chazon Ish second-hand as saying to say hagomel after any flight, and others (the Belzer rav, the Tchubiner rav) secondhand as saying not to say it.