What Is The Most Romantic Song That You Have Ever Listen To?

"Maybe I'm Amazed" (already mentioned) is an incredible love song.

I'm amazed that PM is able to make it through it.

I also like "Sara Smile".

Not certain if the OP's query is meant to include love songs, which can differ from romantic songs.

DeKay

Hats off to Mickeyb for Grant Lee Buffalo and Honey Don’t Think….unique vocal style.
Can’t believe I’m saying this but, 
ELO - Telephone Line
stops me every time.
Unrequited love doesn’t really qualify as romantic…or does it?
Elvis Costello - She is my GFs choice

A few more that I can think of:

How deep is your love - Bee Gees
Words - Bee Gees
To love somebody - Bee Gees
You're my home - Billy Joel
Annie's song - John Denver
My eyes adored you - Frankie Valli

and this is up there too
https://www.youtube.com/watch?v=XqLTe8h0-jo
God Only Knows by Mr. Brian Wilson

Paramour - the only exception (is you)

https://youtu.be/-J7J_IWUhls