Rain Songs

Rain On Your Parade - Duffy

Rainy Night In Georgia - Brook Benton

It’s Raining Again - Supertramp

Raining In My Heart - Slim Harpo

Rain - Dragon (NZ/Aus)

Extended version...

Rain - Uriah Heep

Standing In The Rain - Wishbone Ash

Blue Eyes Crying In The Rain - Levina Records

One More rainy Day - Deep Purple (original lineup)

Raining Blood - Slayer

A Rainy Night in Soho - The Pogues

Make It Rain - Gov't Mule

(Since the OP didn't specify the title should include the word 'rain', but only that it should be a 'rain song': )

Riders on the Storm - The Doors

Rain - Jimmy Somerville

Ride The Rain - Quincy Conserve (NZ)

Sittin' In The Rain - John Mayall

November Rain - Steve N' Seagulls

Fire And Rain - Blood, Sweat & Tears

Saving For A Rainy Day - Mother Goose (NZ/Aussie)

The Rains of Castamere - Serj Tankian (from Game of Thrones soundtrack)

Rain - Madonna

(Again not in the title, but it definitely is a 'rain song')

When the Levee Breaks - Led Zeppelin

Rain - The Cult

Rainy Day Dream Away - Jimi Hendrix

or Rainy Day Dream Away - Randy Hansen Band

Africa - Toto

(Shouldn't it be listed here too? After all the word 'rain' appears more times in that song than in many of those which were included here lol)

Singing in the rain

Haven't gone through the lyrics to see if "rain" is actually mentioned, but it is implicit in a "Storm"

Thunder, Lightning, Rain - Savoy Brown

Blue Drops Of Rain - Corey Stevens