I get that one in 2 notes. I get Motley Crue’s Ten Seconds to Love in the first 3 or 4 notes of the intro. There are a few early 80’s metal songs I recognize in the first few notes.
I feel like I can get most any 80s song in the first few second, but it might be an illusion.
Also, Funky Town.
I’ll name that tune in:
One:
Hard Day’s Night – that chord (and it’s not quite what you think pickers)
I Feel Fine – the feedback.
Money (Floyd not Beatles) – Ker-ching.
Taxman – don’t even have to wait for the song to start, George counts in in a silly voice “One. . .”
**Shine On. . . ** – If for one you can accept a Gminor that goes on for minutes.
Two:
**Purple Haze ** – the devils interval.
I give up the are too many to list.
If you play the original recording, I could id hundreds if not thousands of tunes within a fraction of a second***** (couldn’t most people?). If you just pick out the tune on a banjo you need at least three or four notes to go on but I don’t think that’s what the OP was asking.
*****provided they were recorded before about 1985 when they stopped making music 
I don’t think it’s an illusion, Scott. It only takes me a second or maybe two to identify the majority of the songs I know well, and any song it takes more than 3 or 4 seconds to identify annoys me that I’ve taken so long to do so. I don’t think people are giving themselves enough credit if they think there are a lot of familiar songs they couldn’t nail after hearing just the first second of.
The theme from Hawaii 5-0.
This morning on the radio (as part of a “Hot enough for ya!” set ) they played Tchaikovsky’s Symphony No. 1, which is subtitled “Winter Daydreams.”
The first movement of this is on the Toys soundtrack, on a track called “Winter Reveries.” I didn’t know it was Tschaikovsky, so that was a neat thing to discover.
Here’s a short sample to listen to. Check out the first movement. It has a very distinictive opening.
Steppenwolf’s Born to Be Wild – hard to imagine how anyone could not recognize that crashing guitar intro.
Enesco’s Roumanian Rhapsody #1 (i still sniffle at the thought that my mother somehow lost/gave away a 1955 recording conducted by Enesco himself)
Led Zeppelin’s Rock and Roll – another distinctive drum opening
Tchaikovsky’s 1812 Overture
Rossini’s William Tell Overture (and no, i don’t mean just the part they used for The Lone Ranger’s theme)
Wagner’s Pilgrim’s Chorus from Tannhauser
ditto Ride of the Valkyries from Die Walkure
those are my most remembered, but lots of other oldies rock and selected classical pieces click just as fast.
I’m never sure, with the beat at the beginning, if it’s going to be Iron Man or Slow Ride.
Pink Floyd - Another Brick in the Wall, Part 2 - I can’t think of any other song that starts out sounding like a helicopter.
Pink Floyd - Comfortably Numb - The first note is recognizable and long and drawn out.
Oh yeah, and Bohemian Rhapsody.
Pink Floyd - “Wish You Were Here”
The Doobie Brothers - “Rockin’ Down the Highway”/“China Grove”
“Goodnight Saigon”. 
How could I forget!? Michael Jackson’s Billie Jean.
Porky Pig: L-l-l-lucia de Lammermoor?
Daffy Duck: Audience?
Audience: RIGALETTO!
Sorry, but it was the first thing I thought of.
Beethoven’s 5th Symphony.
I get Lynyrd Skynyrd- Free Bird by the first note.
The opening notes of Iron Butterfly’s In-A-Gadda-Da-Vida have got to be among the most recognizable notes ever.
For anyone who grew up in the 80’s, there’s no mistaking the opening of Def Leppard’s Rock of Ages.
Calling Occupants of Interplanetary Craft-Klattu
It starts with forest sounds with this skip like it was being played on a record player-I can identify it from the first skip about three seconds in
Of course, not many songs start out with forest sounds either.
Just about ANY song by REM (high school obsession), specifically:
“Feeling Gravitys Pull”
“Losing My Religion”
“Fall On Me”
“Radio Free Europe”
And the entire line-up of <i>Automatic for the People</i>.
Also, “Smells Like Teen Spirit” and “Lithium” by Nirvana.
And One’s Sweety, Sweety. First note. Actually, practically anything by And One is easy to identify- Panzermensch, Techno Man, and Get You Closer.
I agree with Coil about Closer, too.
Cocoon, by Assemblage 23.
Let It Be, The Beatles.
Forever, Bruderschaft.
Hooked, by Seabound.
Crabbucket, K-Os.
Small Clanger
People have said that all of the Beatles’ songs are almost immediately recognizable. But I’d agree that “Hard Day’s Night” must be THE most distinctive intro of their songs (or maybe of any song ever recorded).
By the way Small Clanger, for the intro I play a D7sus4. Is that what you play?
As for classical music, how about “The Poet and the Peasant” ?