Unforgettable was written by
Irving Gordon (music & lyrics) in 1951. The song was famously recorded by
Nat King Cole in the same year.

This is how the melody begins. Together with the chords played in the 1st and 3rd bars, it creates such a distinguishable feel that you recognize the song instantly.

These are the chords I just mentioned. The second one is a relatively obscure chord type called
diminished 7. The placement of this chord at this early point of the tune (and with the length of two bars) is rare and unique.
(Lyrics)
Unforgettable, that's what you are
Unforgettable, though near or far
Like a song of love that clings to me
How the thought of you does things to me
Never before, has someone been more
Unforgettable in every way
And forever more that's how you'll stay
That's why, darling, it's incredible
That someone so unforgettable
Thinks that I am unforgettable too.