Mal Reynolds was in a sexless love triangle with Zoe and Inara.
Holmes & Watson?
-JD and Turk <Scrubs>
-Definitely the Crouching Tiger… one.
There’s more, just not coming to mind right now.
As long as we’re adding so many bromances: Chandler and Joey
Peter Pan and Wendy 
Dennis “the menace” Mitchell and Mr Wilson 
Matt Dillon and Miss kitty, unless you want to assume that since she ran a saloon, it was totally on backstage.
Jan and Marsha Brady?
Picard and Crusher
The Odd Couple.
Clarice and Hannibal Lecter.
James Stevens and Miss Kenton in the Remains of the Day (both book and movie).
A BJ is not quite “sexless”.
Frasier & Roz
Norm & Cliff
Mike and Tim (Spaced) - also Tim & Daisy.
mmm, also Shaun & Ed in Shaun of the Dead and Angel & Danny in Hot Fuzz! It’s a Pegg&Frost thing.
House and . . . about half the cast.
Hawkeye and Trapper.
Hawkeye and BJ.
Mary and Murray.
Frazier and Niles.
Kirk and Spock.
.
.
.
Lucy and Ethel.
I love the quote from CSM to Scully in “En Ami”. He tells her “You’d die for Mulder, but you won’t allow yourself to love him.”
Did Wash know?!
Sam and Dean were the first to pop into my head, too. It was amusing when they were pretending to be mental patients, and immediately got split up by the hospital staff because they were too codependent (which freaked them out because, yes, they are codependent).
I always liked Mulder and Scully, too. I’m annoyed that eventually became canon.
Xena and Gabrielle.
Gilligan and the Skipper.
Hiro and Ando.
Who are…?
Not sure if this counts, but I keep thinking back to the movie “Chasing Amy” where Hooper is talks about Archie and Jughead.
Hiro and Ando are the two Japanese characters from Heroes.