The Cascades: Listen to the Rhythm of the Falling Rain.
Or, if your prefer, the Dan Fogelberg version: Rhythm of the Rain.
November Rain - Guns N’ Roses
The Rain, The Park & Other Things - The Cowsills
In the early morning rain.
When will it rain. Jackyl Jackyl - When Will It Rain - YouTube
Well, if flood songs count, there are hundreds of them in blues and folk:
When the Levee Breaks - Kansas Joe McCoy and Memphis Minnie (Led Zeppelin version)
High Water Everywhere - Charlie Patton
Louisiana 1927 - Randy Newman
All these songs are about the 1927 Mississippi flood, and there are numerous more alone about that special flood.
Another:
Save It For A Rainy Day - The Jayhawks
When that I was and a little tiny boy,
With hey, ho, the wind and the rain,
A foolish thing was but a toy,
For the rain it raineth every day.
William Shakespeare, Twelfth Night
Missy Eliot’s The Rain (Supa Dupa Fly).
Which samples Ann Peebles’ I Can’t Stand the Rain.
Daniel Amos - Grace Is the Smell of Rain
Bruce Hornsby and The Range - Mandolin Rain
Sam Phillips - Same Rain
Rain - Taste of Rain
Eddie Rabbitt - I Love a Rainy Night
Eurythmics - Here Comes the Rain Again
Fleming & John - Rain All Day
Madness - In the Rain
Love Reign O’er Me - The Who
Here Comes The Rain Again - Eurythmics
Walking In The Rain - Johnnie Ray
Laughter In The Rain - Neil Sedaka
Bus stop - The Hollies
Stephen Bishop – Save it For A Rainy Day
REM - So. Central Rain
Classics IV – Stormy
Let It Rain - Eric Clapton
ZZ Top - Sure Got Cold After The Rain Fell
Cowsills - The Rain, The Park & Other Things
Truly an odd couple, there!
Another Randy Newman song:
I Think It’s Going To Rain Today
ETA: Best heard in the Dusty Springfield version: https://www.youtube.com/watch?v=jHk5zs4ll44
Enya: “It’s in the Rain”
When I googled for that link, I also found a more recent Enya song, “Echoes in Rain” but except for the title it’s not about rain at all.