Allow save files to be deleted/moved from within the main program (i.e. the save screen)
Why oh Why is file management so awful in Civ 
Allow the use of sliders on the diplomacy screen so gold can be more easily adjusted without having to keep re-entering the amount of gold.
Trading is very fiddly at present
Incorporate some of the CAII features so the game is more user friendly.
Players shouldn't need to resort to spreadsheet applications to get at basic information
Improve the city screen so it gives shields required/remaining and clearly shows # of unhappy citizens after specialists
It's impossible to work this out from the city screen with larger projects or large pops with lots of specialists
Introduce stacking limits based on terrain & technology. Large stacks could suffer attrition damage. There could also be a support unit (or tech) that reduces attrition.
For those that hate the SoD style of play, where is the subtlety
A PBEM map generator that gives all players a fair staring position (i.e. no isolated/inhospitable terrain resourceless starts).
I know you can do this manually but it spoils the surprise if you have a rough idea of what the map looks like.
Difficult start positions in Solo are one thing but in PBEM it's something else!
Increase the number of AI players allowed in PBEM, to accomodate 8 Human players plus up to 8 AI civs.
How many good Mods could be played PBEM except they have more than 8 civs?
Fix the bugs in PBEM that corrupt the trade/diplomacy features.
It's so annoying when you can't trade or have to rewind many turns to complete a game
Show tradable techs for Human players in PBEM, or at least have the option for it.
How many potential deals are missed in PBEM 
Simplify Corruption
When does a courthouse pay it's way?
