I used to spend hours with Civ, be it 2, 3 or 4 (never played 1)
3 was and remains my favorite. The only real drawback is late-game AI invincibility
4 gave me a major sadness when I first tried it, in that it removed the sense of masses, that I had loved in 2 and 3. The idea of a large army went from 150 tanks to 5 tanks or 30 jetfighters to having as many as 3 jetfighters. I hated this at first, this "symbolic" approach to warfare, "I see your one tank. I counter with one artillery cannon and maybe one jetfighter!"
Civ 5 was fine, but all of these allow you to "role play" a nation, be diplomatic or war mongering, develop and grow, maybe play as a peaceful modern nation with a bloody and violent past, making yourself a story. If you were truly unlucky, another nation would launch a surprise invasion, and if you survived it, it would be a significant point in the history of your nation. In Civ 4 I was impressed by an actual naval invasion, taking me completely by surprise, and I remember it even many years later! When you're at constant war, and every single war comes from a surprise invasion, it just stops mattering, and it becomes an annoying nuisance instead, another reason to just shut the game down and go watch tv instead or something...
Again, Civ 3's my favorite, I'd also spend hours "modding" the map and editor. I've made korea-maps, israel v palestine maps, and - of course - north american fallout-themed maps, all of them with units carefully rewritten to make sense in their scenarios. None of them worked very well game-play wise though, and I quickly noticed that thing with modders where they end up never really playing any of their projects, beyond just testing that things don't crash
(This reminds me of my in-total 3 attempts at creating a modern world map for HOI2. What an ass-pain that shit was... )