What is the greatest love story of all time?

I may be a pessimist, but Amour and Blue Valentine for me… and the Before Sunrise/Sunset/Midnight trilogy.
As for young love, the Spectacular Now and Like Crazy.

I'd have to say the couple in UP. They grew up as friends, loved each other, dealt with real life problems, couldn't have kids, still loved each other, and basically were your normal but loving every day couple.

No truer love than theirs, IMO. A lot of movies depict love horribly.

-Pride and Predujice
-Cinema Paradiso
-Ana Karenina
-Harry and Sally

Celine and Jessie Go Boating in Before Sunset

Pride and Prejudice, Eternal Sunshine of the Spotless Mind, Casablanca, The Ghost & Mrs. Muir, The Quiet Man, Two for the Road. This is off the top of my head.

Here is one that hasn't been mentioned I don't think how about Baby and Johnny from Dirty Dancing this is one of my faves.

Here's one which I doubt anyone else has said.
Sam and Jill in Brazil.

Les Enfants du Paradis (1945)
Le Notti Bianche (1957)
Brief Encounter (1945)
Waterloo Bridge (1940)
Bright Star (2009)
The Artist (2011)
In the Mood for Love (2000)
Broken Blossoms (1919)
Devdas (2002)
Letter from an Unknown Woman (1948)
In a Lonely Place (1950)
The Cranes are Flying (1957)
Summertime (1955)
Written on the Wind (1956)
The Wings of the Dove (1997))
The Age of Innocence (1993)
Camille (1936)
Cairo Time (2009)
Liebelei (1933)
Casablanca (1942)

To name a few, anything better than the hack called The Notebook.

Honey, you should see me in a crown