In the auditory field, the principal association with airlines in the mind of the public is that five-letter word "noise". However, air travel evokes enough pleasant perceptions that it has been alluded to a number of times in popular songs, although the more cynical among you may note that there has been less of this in recent years than in times past.
A notable historic occurrence was Frank Sinatra's "Come Fly with Me" album, which featured artwork of TWA Constellations on the album cover, in line with its 1958 release, essentially just before the jet age began in earnest. In reality, it's primarily a musical journey around the world, extolling a variety of evocative locales, rather than the virtues of air travel, although "Around the World" and "Let's Get Away From It All" do reinforce the idea of travel. The album's title makes it clear that the "Chairman of the Board" isn't considering making these journeys by steamship, however.
More recently, in 2004, singer Michael Buble issued his own version of a "Come Fly with Me" album, but with the exception of the title song, the tracks are different from the Sinatra original, and don't have a travel theme.
The nod for best promotion by an individual airline in this genre goes to British Airways' predecessor BOAC, which managed to get its brand mentioned in two pop songs. In Bobby Bloom's "Montego Bay", the first line leads off with "Vernon'll meet me when the BOAC lands", conjuring up images of vacationers arriving in Jamaica aboard elegant VC-10s.
Similarly, the Beatles' "Back in the USSR" cover of Chuck Berry's "Back in the USA" starts off with "Flew in from Miami Beach BOAC/Didn't get to bed last night/On the way the paper bag was on my knee/Man I had a dreadful flight" (and omits mention of the necessary stop and connection at Heathrow, to get from MIA to MOW). Incongruously, the sound effect heard a number of times during the recording sounds suspiciously like a Rolls-Royce Dart turboprop, not the Rolls Conways, or possibly, Pratt & Whitney JT3Ds, that "the lads" would have experienced on their 1960s transatlantic journey on the British carrier. (Chuck Berry's original version is somewhat more generic, noting that "We touched ground on an international runway/Jet propelled back home from over the seas to the U.S.A.")
On a multi-modal note, "The Letter", by the Boxtops begins with the demand to "Gimme a ticket for an aeroplane/I ain't got time to take a fast train". In what could be described as an airline yield manager's dream situation, this customer states flatly that "I don't care how much money I gotta spend/Got to get back to my baby again", all because "my baby just wrote me a letter". Apparently, this was quite a passionate composition; airline encouragement of similar documents e-mailed to young, single frequent flyers might do wonders to stimulate airline revenues today, although it should be noted that "fast trains" have made significant inroads in a number of shorter markets since the song was written. And for that matter, a letter is probably not something to be expected often in today's communications spectrum; do you suppose a tweet could have the same impact?
There are other examples of airline/pop music combinations, an obvious one being Steve Miller's "Big Jetliner". While the title of "It Never Rains in Southern California" gives little hint of any airline connection, the opening line -- "Got on board a westbound seven forty-seven" -- provides a nice plug to the Boeing product, and also dates itself, since there hasn't been a lot of 747 service in the U.S. domestic market in a number of years.
Some other airline/pop music connections include references to the British 1960s group the Dave Clark Five as the DC-5 (and I've seen a picture of a Convair twin-engine prop that they used for travel with that emblem emblazoned on it); also from the U.K. was a female singing duo that billed themselves as the Caravelles, after the French twin-jet airliner. For that matter, before they became the Starship, there was the Jefferson Airplane, which Virgin America recognized by naming an A320 in its fleet for the group, including having singer Grace Slick present for the ceremony.
There are several songs using either the "I'm going away" or "I want to get back to you/home/etc." theme, including Gordon Lightfoot's "Early Mornin' Rain", with it's "Big seven-o-seven set to go"; and Crosby, Stills & Nash's "Just A Song Before I Go". Unfortunately, the latter's reference to "Travelling twice the speed of sound" is no longer possible for civilians. Finally, in the same general category is the Peter, Paul and Mary classic "Leaving on a Jet Plane", probably the best known of the type of song being considered here. Anyone want to add others?
And while not in wide circulation, there is a series of CDs titled "The Glorious Sound of the Big Props" (piston & turbo) produced by Aero Dynamic Recordings in the Netherlands. One person's noise; another person's music...