Eli Bendersky's website From what I've seen so far (going through the tutorial and playing for another couple of hours myself) Civilization 4 is a terrific game. I still haven't fully adapted for the things that changed since Civ 3, but some initial impressions are now formed.
First and foremost, the graphics. When the first news of Civ 4 started coming, I joined the sceptic train, thinking that a game like Civ doesn't need good graphics. Well, I must admit I was wrong. The beautiful full-3D world (with zooms and camera rotations) of Civ 4 is amazing, and adds a lot to the gameplay. Everything is more realistic, and for a change you feel creating something *real* and not just tiled icons on a tilted map.
The user interface is very well-thought and convenient to use. Everything is accessible in a single click / keyboard shortcut, and the quick city view is very useful.
Also, I must say that the "civics" are cool and IMHO preferable to several hard-coded goverment types. If goverment would be that simple, political science wouldn't be a University degree. A goverment is an amalgalm of "civics" - approaches to issues like economics, population, religion, research, etc.
From reading in the manual a bit I see that Civ 4 has a lot of advanced features I haven't come to need yet (I didn't complete a game yet, my first game is now in year 920 BC) but I'll love in the later stages - normally designed city build queues, many options for worker automation, unit stacks / group orders, etc.