If I were to pick some things from previous versions that I feel should have become a staple of the series it would be the following.
The most pivotal event from Civ 1 was a large empire splitting because of civil war. Why this was not used in any of the other games is beyond me since it was always something that kept the big dogs in check. Too big and/or too unhappy and a section of your civ would split off forming it's own civ similar to puppet civs from IV but generally quite hostile to the parent civ. This was an epic turn of events and always changed the way the game continued since it usually happened to the player in the top spot. Loved it when it happened to the AI but I can remember plenty of games where it totally ruined my warmongering and brought my offensive to a halt as I had to supress the rebellion which had erupted in my own empire.
Animated advisors that would argue with each other from Civ 2 sticks out as another wonderful addition to the series that I would include. Similiar to what's in 5 now but different in that they would debate with each other about the best possible way in which to improve your empire. Voiced over stereotypes (geeky science advisor, buffed up military advisor, etc..) with quality acting led to wonderful exchanges that I still remember quite clearly even years later. They changed their attires and comments as the ages progressed and were rarely in unison on which path to take but man was it amusing.
The extensive Civopedia which listed detailed real world history about units, leaders, civs, wonders, etc... from Civ 2 and 3. I think I learned more about history from reading the flavor text of particular entries in the civopedia than I was taught in all of my years in history class.
I miss buying enemy units with gold and a diplomat/spy unit. It was Civ 2 and I remember it saved my arse on several occasions when I had put too much into commerce and not enough into a military. While horribly expensive to do it made for an interesting way to acquire units you could not otherwise get because of a lack of resources or technology.
Enemy units that spawned when you razed a city always made for an interesting turn of events. I never liked it when they spawned from TAKING a city but it felt right when they spawned because you burned it to the ground. They were never a large threat (since the rebel units were generally one era behind) but if you sacked a huge city you could end up spawning a horde of them and they were quite annoying indeed.
One of my favorite features from Civ 3 was the army units and how you could custom build them and even get wonders that adjusted how many units you could load into them. It was fun to mix and match what you threw into the stack and it was another one of those "Why didn't they keep this option" when I moved to Civ 4.
Civ 4 has a ton of great features in it but I really miss the wonder videos above all else. I enjoyed seeing them constructed as it represented the culmination of the 10-40turns that I had spent building the freaking thing. The music was nice but after you spend 30+ hours listening to a game's soundtrack I tend to prefer Pandora or an MP3 player.
These items would be in my perfect Civilization along with Civ 5's graphics and hex layout. The added Natural Wonders are a pretty nice edition too!