I haven't played Civ 4, but Civs 1 - 3 are all classic games that I have spent months and months of my life playing.
Medieval Total War is also an excellent game. For those of you have played both, which do you think is better MTW or MTWII? The second obviously has some improvement over the original like much improved battlefield graphics, improved crusades, improved religion etc, however overall I found MTW to be a much more immersive game.
The cartoony graphics in the strategic map for MTWII were a little too much for me (don't get me started on the stupid "Yes my liege"). The "improved" strategic map in the second was good in theory, but the AI didn't seem capable handling increased demand that the map placed on it. In the first one the Risk style map allowed every countries moves to be executed simultaneous, while in MTWII my opponent's armies would stand completely still while I did laps around them. A step back in my opinion.
Some Classic games that I'm fond of: X-com, Master of Orion, Imperialism II, Conflict Korea, Pirates, Warlords.....ah the memories.