I just threw together this tutorial for being able to play without your disc.
You'll need this program (which is rather widely used and generally scanned and assumed to be bug free, don't let its non-American origins scare you):
Anti-Blaxx -
http://mb-lock.copybase.ch/English/Index.htm click the download link on the left and choose anti-blaxx 1.17.
Once this is installed and running you should see an icon that looks like a disc in the tray at the bottom right side of your screen. Right click it and choose settings. Leave everything alone except for these settings:
Near the bottom of the window, click the Protection dropdown and choose SafeDisc. A window will come up saying it couldn't detect copy protection, disregard it and click ok. To the right of that, click the three dots button to the right of the edit box labeled "Game:". Navigate to your Civilization4.exe file, this is by default stored at C:\Program Files\Firaxis Games\Sid Meier's Civilization 4\Civilization4.exe . After you click ok in this window a box will come up asking for the game name... this can be anything, but just type "Civilization 4" and click ok.
You should be done. Click Close (not Exit which quits the program). Rightclick the cd icon in the bottom right of the screen again, hover over Run game, then click Civilization 4.
This is such an extreme inconvenience to have to have the disc inserted all the time..it's worth violating the EULA over. I'm new to these forums and don't know whether this will cause me to get banned to write this, or whether the post will be pulled, or whether nothing will happen

(and I don't intend to break any rules, I just haven't seen any that apply to this situation). I hope it'll help some people out.
-Cliff