A few things for me (in no particular order):
1) music.... I liked civ III and II music... don't like IV's at all. Just not a fan of classical or tribal music.
2) landmasses - no fun, boring, landmasses. The map generator just makes big blobs. Not many chokepoints, or harbors, or inland lakes.
3) magic - no magic. The landscape is so intriguing, and I love the initial exploration phases, but their are no ruins, no mysterious caves, no caverns. I can't explain it, but the game feels like it would be much better as a fantasy game. Maybe it's the flags all the units carry around.
4) been beat too many times.... I played on monarch about 40 times. After losing the 40th, I just quit.

(the playtester probably assumed in this situation some of us would try an easier level...

)
5) Something about diplomacy.... like you cannot trade resources for technologies.
6) No tactical battles..... I know it is not classic civ style, but with the new unit system, I would have liked more control over the ways my armies fight.
7) cartoon friends and enemies... the leaderhead art was a downgrade, they are charicatures. If I am playing a game for hours, I am serious. The enemies and friends are too funny... like Alexander always looks drunk.
8) colors... I have to be red Japanese, or mod the game. I really would have liked custom colors. Then I could have had black samauri or green samauri.
9) Icons... the icons in the advisor screens seem smaller than civ III, and less neat, now they just have numbers next to them.... instead of being stacked like in 3.
10) I know alot of this was sacrificed for multiplayer. Civilization would need a
radical break in thought if it were to ever be a multiplayer game. That did not happen, and soon civ IV's multiplayer will be a bunch of boring fast 2-player ladder games. Firaxis should have AT LEAST set up an official ladder and website. If they had, they could have control over MP, how it was played, ranked, etc... and give it an "official" feel. This "official" feel is very important to many players. It's why I never played any other historical mods in Civ III or Civ II. If I Was going to play a historical game, I only wanted to play the official one.
That said, I still think Civ IV is great fun, and I am not playing it any more for personal reasons. When the SDK comes out, and if it has a graphics conversion tool, I may be interested again.... for modding, of course.
EDIT: One more thing, ever since I decided that politics are for the birds, my interest in history has seriously waned, so a historical game is really not my cup of tea any more.