I know lots of people thought Rey would be Luke's daughter, myself included, but obviously that's not the case.

So, did Luke remain single?

Well. We don't know. It seems that way. 
Now you might say, "well, the Jedi code forbids romance." But I believe that Luke abolished the old code. It was very messed up, and honestly, if the whole "no attachments" rule hadn't existed, I think anakin would not have turned to the dark side in the first place, because he wouldn't have to hide it and would have been more willing to tell obi wan about his nightmares. So I think he allowed for romance in his new Jedi order.
So, if romance was allowed, did Luke find any? I personally think he did. Luke seems too lovable to stay single. But where are they in the newer movies? I have a theory, but it's sad. I think that his wife and kids were killed when Kylo and the Knights of Ren rebelled and destroyed the Jedi academy. It's a very heartbreaking theory, considering how much Luke has been through already, but it would make sense why Luke would remote himself. Not just guilt, but in deep pain in mourning his family. He blames himself for their deaths so he hides himself so that he can't hurt anybody else's family. In watching the last Jedi I felt like there should have been a deeper exploration into why Luke was the way he was. He was vastly different from when we last saw him in return of the Jedi. And to me, just saying "he feels guilty about Ben's turn to the dark side" just doesn't seem like a good explanation. Obi wan lost anakin to the dark side, but he was still willing to train Luke.  But the idea that Luke lost his family to the purge adds a whole new level of emotion and deepness to him. It would also explain why he sacrificed himself, because he could have still fought the first order and lived. But maybe he just was looking for a way to be reunited with his family again.

Again, this is all purely my imagination, but I think it makes sense. It does make Luke's story even more sadder than it already is, but, to me, it gives more clarity on why Luke is the way he is in the last Jedi. Again, while I do think ben's betrayal affected him, it didn't seem like that by itself could be enough for Luke to go hide away for years and years.

Let me know what you think of this theory in the comments.