I happened to catch “Jet Airliner” by the Steven Miller Band on a classic rock station. Nothing deep, but a really nice song.
One line is “as I get on the 707”, a reference to the Boeing 707, and wondered if there are other popular songs that mention a specific type of plane?
“Dallas From a DC-9 at Night”
Electric Light Orchestra mentioned 747s in two of their songs:
It Never Rains in Southern California
Got on board a westbound 747
♫ Out on runway number 9
Big 707 set to go… ♫
Evocative lyrics by Gordon Lightfoot:
"Early Morning Rain"
…
Out on runway number nine big 707 set to go
But I’m stuck here in the grass where the cold wind blows
Now, the liquor tasted good and the women all were fast
Well, there she goes, my friend, well she’s rolling down at last
Hear the mighty engines roar - see the silver bird on high
She’s away and westward bound - far above the clouds she’ll fly
Where the morning rain don’t fall and the sun always shines
She’ll be flying o’er my home in about three hours time
…
You can’t jump a jet plane like you can a freight train
So, I’d best be on my way in the early morning rain
There’s Saxon’s “747 (Strangers in the Night)”.
“We got a 747 coming down in the night
There’s no power, there’s no runway lights…”
And of course there’s this one from Queen.
‘Johnny Come Lately’, Steve Earle
♫ My P-47 is a pretty good ship
And she took a round comin’ cross the Channel last trip… ♫
You beat me to this. After years of listening to this song, I was pleasantly surprized when I got to actually see one of these at the Smithsonian Air and Space museum in DC (the one on the mall, not Udvar-Hazy). Very cool to see in person (and a bit smaller than I was expecting). I had to see if I could identify the “clustered R4M quartets” 
Stukas Over Disneyland, The Dickies
I actually don’t generally listen to country music, but I heard this song on some TV show and remembered the reference to the 737 (and Gulfstream G6).
Wot, no love for PP&M? 
Creedence Clearwater Revival had experience with a
Seven Thirty Seven comin’ out of the sky.
Oh! Won’t you take me down to Memphis on a midnight ride,
I wanna move.
Wilco - “Dash 7”
Great song, but it doesn’t mention a specific model of jet plane. 
Chuck Berry’s ‘Run Rudolph Run’ mentions a Sabre jet.
Of corse it does. The lyric is in my post.
♫ Out on runway number 9
Big 707 set to go… ♫
It’s also in @K364’s post right after mine: ‘Out on runway number nine big 707 set to go’
Apologies – I thought that “Wot, no love for PP&M?” was referring to “Leaving on a Jet Plane.”