Probably any classic rock song or alternative I’ve heard repeteadly on the radio. Certainly almost any Allman Brothers tune - at concerts, if one of the guitarists idly strums a chord or a few notes between songs, I know what’s coming next.
A couple of months ago I heard “One Headlight” by The Wallflowers while I was shopping. I knew the song by the drumbeat, which surprised me because I never thought that opening drum part was very distinctive.
It’s spooky when the note is truly a single note, and not played on the original instrument. I remember an Opera Panel doing a quiz and the toughness of the “Name That Tune” segment increased until they came to one note - an a-flat. “Che Gelida Manina” said the expert - bingo!
REM’s “Crush With Eyeliner”
Status Quo’s “Pictures of Matchstick Men”
The Beatles’ “I Feel Fine”
A few I can do:
The themes to “Hogan Heroes” and “The Twilight Zone”
Lots of car horns must be in the key of G - I don’t know how many times I hear a honk and my mind instantly begins humming “The Word” by the Beatles.
(Yes, I know the song is actually in D - but the opening piano notes are a G and B.)
Sorry to break your bubble, but you-all aren’t identifying the song by one note, but by the sound you hear, which includes acoustics, timbre, orchestration, waveforms, overtones, and maybe rhythm if you are listening to the intro before the first note.
Try this one: the one note is “A”. What tune is that?
That’s right…it could be any tune you name, because every song begins with a single pitch and any song could be played in any key.
“My Girl”
London - The Smiths
Anarchy in the UK - Sex Pistols
Holiday in Cambodia - Dead Kennedys
Right–I know I would fail at Name That Tune because they would just play the note, not the exact-sound-from-the-recording-I-know.
Strangely enough, every time the classic rock station plays “Freebird”, I hear the opening organ and think it’s gonna be “Whiter Shade of Pale”. I’m actually pleasantly surprised when it turns out to be “Freebird”, because I don’t like “Whiter Shade of Pale” at all. Never have been able to figure out why it was a hit.
If I remember correctly, most of the identification process on that show came from analyzing the verbal clues; hearing the notes was just a way to verify your conclusion. The people who said, “I can name that tune in one note” usually had it figured out already and probably didn’t even need to hear the note, but they couldn’t say, “I can name that tune in no notes”.
Interestingly enough, rhythm is often more important than melody when it comes to identifying a tune. My mom was at a music teacher’s conference some years ago where this was demonstrated. The speaker played the notes of “The Star Spangled Banner” on the piano (without naming the tune), but in a completely incorrect rhythm and asked if anybody could identify it. Nobody could figure it out. Then she played the rhythm of the song using only a single note, and everybody got it immediately.
I’m probably setting myself up for failure by arguing music with someone named Musicat, but can’t note also refer to the entire set of: 1) printed note head + stem, which includes both the pitch (“A” “G” “C flat” etc), 2) duration (quarter note, whole note, etc) and 3) other information (crescendo, vibrato, etc).
I mean, if my music teacher handed me a sheet of music and said “play the first note”, I would play it all, not just the “A” by itself.
The album version of Ben Folds Five’s “Underground” starts with a single identifiable note. I won an awesome prize and the awe of all my friends when I got it at After Prom. Blew the DJ away, since it was a huge radio hit but no one (but me) knew the album version.
And yeah, it’s not really a note it’s a chord.
I think some people wouldn’t know it from just the first note (which is a very low tone that lasts for several measures before the trumpet comes in).
Hey, no need to feel inadequate. 
I guess we need a definition. If you put “define: note” into google, most of the defs refer to something other than music, but I think this one hits the spot: “a notation representing the pitch and duration of a musical sound…” Of course that’s only for music notation.
If you define “note” as only a pitch, not a timbre, not including overtones or wave-shaping characteristics, then an A is an A (sorta like Ayn Rand, but with a differnt meaning).
The more characteristics you include in the definition of “note”, the more it can be associated with specific tunes or recordings. I, myself, can recognize most of the songs mentioned here within a few fractions of a second of first hearing them.
Merriam-Webster uses the same wording for “note”, but gives a synonym as tone:
So I guess it could go either way; one def includes timbre, one is limited to pitch only.
I am reminded of the guess-the-song contest on WKRP, where, due to an error in announcing too much prize money, the DJ staff tried to make the sound clips as short as possible and run them together so no one would guess them all. Unfortunately, the first caller got all of them right except one, so their scheme was off to a poor start.
Since I’m the OP and everyone but Musicat got the idea without further explication, I fear this will come across as harsh, so please understand, it’s just a clarification:
Yes, Musicat, you’re entirely correct in the analytical sense. You have simply totally overlooked that we’re having fun here, and we’re not talking about an abstract musical score played on any random instrument from sheet music.
As everyone else figured out, we’re talking about well-known (to varying degrees) recordings of these songs.
Rite of Spring by Stravinsky.
Rhapsody in Blue by Gershwin.
And click on this link and close your eyes…