And Deborah Kerr and Yul Brynner in The King and I. Ooooh, hot hot hot.
Miss Kitty and Marshal Dillon in Gunsmoke
Alan Ladd and Jean Arthur in Shane
Irene Adler. Ha! Holmes and Watson were the couple in that series!
Ernie and Bert.
Norm and Cliffie.
Fred and Barney.
Wilma and Betty.
Edina and Patsy.
Laverne and Shirley.
This gets my vote.
Uh, surely it’s Romeo & Juliet.
I have to disagree. It is very strongly shown (quite clearly in the film version) that Sam and Frodo had a very deep platonic love for each other.
Didn’t they consumate?
“Unconsummated?” R & J? Those two got married, spent the night together, and humped like weasels before Romeo split for Padua.
If they didn’t, I’m remembering it wrong.
Which was of course in response to Rocketeer. Note to self: type faster!
I see we’ve moved from unrequited love to straight-up slash pairings. So to keep with the spirit:
Murtaugh & Riggs (Lethal Weapon)
Clarice Starling & Hannibal Lecter (Silence of the Lambs…sorry, Hannibal don’t count.)
Jack Crawford & Hannibal Lecter (Manhunter/Red Dragon)
Capt. John Miller & Pvt. James Francis Ryan
Vince & Jules (Pulp Fiction)
Mr. Pink, Mr. Blonde, Mr. White, Mr. Blue & Mr. Brown in a circle with Nice Guy Eddie as the “pinion head” (Reservoir Dogs)
Marge Simpson & Moe the bartender
Marge Simpson & Ned Flanders
Marge Simpson & Barney the drunk (and so on…)
Ron Weasley & Hermione Granger (so far)
Tom Sawyer & Huckleberry Finn
Jack, Ralph & Piggy from Lord of the Flies
uhh…maybe I should stop now. 
Who?
Archie and Veronica. She was just using him, anyway.
We Rhymers don’t acknowledge the existence of that film, for, if it had existed, it would surely have sucked eggs. ;j
Those of you who insist on referring to it are clearly madmen. Madwomen. Madpersons. Whatever.
We prefer Mentally Atypical Persons. 
A strictly platonic one: Eric (the narrator) and Katz in All Quiet on the Western Front. The scene where they’re roasting the goose…
In the books they’re more of a couple. He even kinda proposed once, but she turned him down because she didn’t want to be stuck at home while he was out solving cases. Figured they’d be closer the way it was.
pwn3d! 
Rick & Sam from Casablanca
Slash is nice, but let’s not confuse it with the work it is based on.
Once again, slash is nice, but … 
What’s this? Slash slush?