They were never actually in a relationship! They started dating after Sub Rosa (Season 1) then things went pearshaped after McGee asked were their relationship was going and Abby was happy just to leave things as they were! They only dated for half of the season!

At the end of Season 8, however there is a very tender moment between the two of them and McGee tells Abby 'If something ever happened to you I would..." which indicates that he still has feelings for Abby and worries about her while also giving the hint that he cares and wants to protect her.

YES

We have gotten confirmation of the McAbby ship is in season 12's "Semper Fortis".

McGeek: I know what you're thinking of doing and I just want you to know that I think it's premature.
Abby: Okay, McGee, I know that we used to... and we don't anymore, and it's been a long time. But, uh, this is kind of private and sort of none of your business, so...
McGee: Abby, come on.
Abby: If I want to break up with Burt, that is my decision.

This is in reference to an earlier conversation, referring to Burt as "Mr. Two Months". Later turns into this conversation.

McGee: All right. Well you should probably know that Abby and I used to date?
Bishop: Ew. Like, each other?
McGee: Yeah. Bishop: Wait - isn't that a violation of rule 12, never date a....
McGee: It was a long time ago. After we'd broken up, one night I went to her lab. Found a scribbled piece paper; a list. Potential boyfriends had to fulfill certain conditions by a pre-arranged date or else, goodbye.
Bishop: Such as.
McGee: Things started off relatively normal: opening the door for her, flowers, putting the seat down. Then around number 8, it gets uh... Bishop: What?
Bishop: Does she know you have these?
McGee: Yeah she wasn't happy when she found out.
Bishop: These are all very... specific.
McGee: Yeah.
Bishop: These ideas apply to you?
McGee: No those rules weren't in place when we were together. At least I don't think so.
Bishop: What's with the two month cutoff?
??: Abby's sabotaging herself. I've seen stuff like this before.
??: We have to talk to her.

First on-air confirmation of the relationship that happened in Season 1, ending early season 2. Of all the stolen glances and moments the two shared. And McGee's possessiveness later on. Ever since then, Abby has been a serial dater.

There was a thing between them, but they both decided that a romantic relationship was impossible because they worked together. As did all the NCIS agents including Gibbs who was once romantically involved with his Late Boss. Cmdr. Shepard. Similar to Dinozzo and Ziva, who we all saw had romantic feelings for one another. It just isn't good for the team like when Palmer hooked up with a terrorist that nearly destroyed the team.