Is there any way to make the computer take there turns faster?

[Saxon]

MX1

I am afraid there is not much you can do to speed things up. As your empire grows, so do the computer empires, so the AI has to make more and more decisions. This takes the computer longer to compute.

You could upgrade your machine or browse the web, like some other people do between turns.

[CW]

Wipe out the AI players early on, so they don't grow big enough to slow down your computer! :P

[Atrocities]

You can set the game up in the option window to make rapid fleet movements. That helped my game speed up a tad. (DO NOT SHOW SHIP MOVEMENTS)