That was Janeway and Paris.
Chakotay suddenly had a ‘they will’ relationship with 7of9 in the very last episode, even though there had been no foreshadowing of it whatsoever.
I was going to say Josh and Donna from The West Wing, but I read the synopsis on Wikipedia and apparently they did. I had stopped watching by then.
Sally Field and Ron Liebman in Norma Rae.
Then they’d remain a ‘will they or won’t they’, since the possibility wasn’t cut off. Just the chance that the audience would see it.
Mulder and Scully on the X-Files?
They did - and then inexplicably announced it to the entire bar for no reason - but it didn’t really take.
Umm…they had a baby together, so I think it was pretty much “they did.”
It was brief, but Friends teased a Joey/Rachel hookup late in the show’s run before landing firmly on “They Won’t.” There wasn’t a lot of chemistry there anyway; they were wise to put the kybosh on it.
Sam and Diane did have a relationship going there for awhile, and it was indeed physical. Only later, oddly enough, did we get the endless back-and-forth, before Shelly Long left the show.
Benson and Stabler from L&O:SVU
StG
Not a TV show, but how about James Bond and Moneypenny? Must be the longest “Will they won’t they” going
Beauty and the Beast (the TV show), i.e., Catherine and Vincent. Yes, in one episode they “mystically” kissed, but that was it.
How about Picard and Crusher? Did they ever get together?
By the way, I meant Beverley, not Wesley 
Woo!
In web comic world Marten and Faye from Questinable Content. The author set it up like they would but the focus became why Faye can’t. A much more subtle piece of writing than expected.
According to the finale, yes they will. Then they won’t. But since Picard is now aware of the possible future, maybe they won’t. And then they will.
Maybe.
In Dawson’s Creek, Joey ended up with Pacey, not Dawson.
This may not fit the category precisely, but…
Kevin Arnold pined away for Winnie all through The Wonder Years, but in the last episode, he reveals that they split up and he married someone else.
Tony Danza and Judith Light had still never committed to anything, as of the time Who’s the Boss? went off the air, had they?
The series isn’t over yet, but on Treme:
In the second season, Janette (Kim Dickens) and Delmond Lambreaux have some scenes together in NYC where they had an amazing level of chemistry together. I thought for sure they’d hook up but then nothing came of it.