First and foremost, ability score damage as a special feature of selected monsters. I have done this sometimes and it works better and more easily in 5e than in 3e!
Somewhat related, but not easy to pull off properly, would be level drain. This definitely requires some thinking, I wouldn't probably bring it as-is into 5e.
An extended skill list inspired by 3ed would be interesting. I have already allowed players to make up some skill that isn't in the PHB list.
Prestige classes in their original concept, i.e. DM-designed and setting-specific alternate high-level progressions that could be granted as a reward and tied to the narrative, could definitely fit in 5e without conflicting with subclasses. This is not something I have tried, and would definitely require some work.
I also think that Weapons of Legacy and Book of Nine Swords could provide interesting additions.