Hmmm...

Adele - Set Fire to the Rain. My favourite Adele track. When I heard it, I knew she was perfect for a Bond song.

Eurythmics - Here Comes the Rain Again.

A-ha - Crying in the Rain (covering the Everly Brothers)

Travis - Why Does It Always Rain on Me?

Garbage - I'm Only Happy When It Rains

Guns N Roses - November Rain

Madonna - Rain. Not one of my favourites, to be honest, I much prefer her 1984 - 1990 material.

Lady Gaga & Ariana Grande - Rain on Me.

Pet Shop Boys - Domino Dancing. A bit of a stretch, but purely for the lyrics "I heard the thunder crashing, the sky is dark, and now a storm is breaking within my heart". Plus I'm rather partial to the girl in the video; the glorious, full version of which can be found here: https://www.youtube.com/watch?v=J-LG9KVcc9E