Civ 1 & Civ 2 had Civil Wars if a Capital was taken, Civ 3 had a Plague & City Flipping system, Civ 4 also had City-& tile-Flipping, as well as events in BtS, & Civ 5 BNW had cultural pressure leading to revolts, particularly in case of Ideologically opposed Civilisations.
I'd like to see Civilisation take all of these past mechanics, improve them significantly, & put them back into the game. Take the best elements of the Civ 3-Civ 5 Cultural Pressure mechanics, & merge them into a Civil War mechanic a la Civ 1 to Civ 2. Take Civ 3's plague system & Civ 4 BtS's Event system & make it significantly more nuanced (so that past player actions play a bigger role on whether events-good or bad-trigger, & always give players multiple choices (3-4) on how to respond to every event. Oh, & bring back the Vassalage System from Civ 4 & the Ideology system from Civ 5.
Lastly, it'd be nice to have a strong, in-game impetus for Civilisations to set up colonies on distant lands. Maybe resources that are unique to that land mass/continent, or a bonus for resources on different land-masses.