They aren’t as common as sexual love affairs–at least not in fiction–but they do exist. What are some good examples?
In television: Mary Richards & Lou Grant were certainly in love, but never really did anything about it. Angel was much better when our favorite vampire with a soul was merely Cordelia’s soul mate, not pining for her. Anybody else got one they care to name?
Butch Cassidy and the Sundance Kid
Gotta be Mulder and Scully on X-files.
Didn’t she have his kid?
I dunno. I stopped watching after Mulder left …
Cyrano and Roxanne.
Ivanava (likely butchered spelling) and Marcus from B5
Janeway & Chakotay from Voyager
Ivanova.
G’Kar and Londo Molari.
Gilligan and the Skipper.
Bob Harris/Charlotte, in Lost in Translation. Especially if you look up what he whispers to her in the next-to-last scene, on the Tokyo street.
Frodo and Sam from The Lord of the Rings. My favourite, though, would be Heathcliff and Catherine in Wuthering Heights. Err, well I suppose that’s up to debate. He did dig up her corpse at one point. We don’t know for sure if he didn’t… you know. Yeah.
That’s all I can think of.
John Steed and Emma Peel in The Avengers.
Stevens and Miss Kenton in The Remains of the Day. How restrained. How proper. How British. How unbelievably hot for each other.
The unconsummated love affair that initially came to mind was Miss Kenton and Stevens from The Remains of the Day. Some of the scenes between the two of them just kill me.
You think that was unconsummated? You poor, naive, bastard. 
Dobie Gillis and Zelda Gilroy.
I’m curious, what have you found? I can only find Sophia saying it’s intentionally ambiguous, and he says whatever you want him to have said. (Please spoiler tag it if you know otherwise!)
I’m going to say this one more time:
FRODO AND SAM WERE NOT IN LOVE!!!
Not that there’s anything wrong with that.
Sam was in love with Rosie Cotton. RO-SIE COT-TON.
I’ll agree with you there.
Perry Mason and Della Street.
Damn! I knew someone would beat me to this…
coughBeard!cough
I don’t remember if Mal and Inara ever consummated anything on Firefly, but that would be one of my nominees.
First, though, would be Thomas Mann’s main character in Death in Venice.