The Apex of Civ
Now, Civ IV *easily* takes the crown for best of the series. It smartly builds upon the new features added in Civ 3, removes stuff that used to be a pain, and adds fun new features. Soren Johnson said it was "1/3 old, 1/3 modified, and 1/3 new":
1/3 old: the premise of the series is the same. Build cities, units, improvements, movement points, improve land, etc. Diplomacy is much the same as Civ3, as is the culture system.
1/3 modified: resource system greatly expanded, combat tweaked, upkeep costs changed to rely on number of cities, tech tree has 'or' paths, siege units prevent stacks of doom, etc.
1/3 new: religion, trade routes, unit promotions, health system, civics
It's amazing that all of the new additions add to the game. Religion is useful in many strategies, particularly cultural and diplomatic victories. Civics allow you a lot more flexibility in persuing your goal, instead of hardwired government choices. Trade routes add depth and options for building your economy. Unit promotions allow you to customize your armies for a purpose (specialization is a theme throughout the game). And the health system gets rid of the awful pollution mechanic and replaces it with something fun and interesting.
The modifications really make the game more fun, also. Resources were a fantastic addition to Civ3, and here they go full blown. In addition to enabling you to build certain units, resources can also improve health conditions and add to overall happiness. Also, the city maintenence is much easier to figure out now, and the ridiculous corruption aspect has been completely removed.
The negatives about Civ4 are mostly technical. The early revs of the game were unstable and not at all prone to CTD. The latest patch (1.61) seems to be pretty stable - no crashes yet, although it still will freeze for short periods of time. In the nit-picky column, the Civilopedia is pretty poor...
But that leads into the incredible customization options of the game. Modders can change literally anything, from just adding a new unit or building, to entirely modifying the core rules of the game! There are great Civilopedia mods out there (check out civfanatics.com).
Civ 4 is the ultimate Civ. I can't fathom what Firaxis will come up with for Civ 5, but it will be hard to top this one.