What happened with the Facebook Timelines?

No idea... I never got the update.

Maybe they were scared of Google+ at the time and made the announcement a bit too early to keep Facebook in headlines. Or they just backed off when there wasn't positive response to it.

I believe they are still in battle with a company that creates similar "timelines" and has ownership over it.

I got an early sign-up to the timeline layout and I still my profile working with timeline...but only other early adopters get to see my profile with the new layout, everybody else (about 99% of my facebook friends) still see my page with the classic layout... at least it looks cool to me.