Civilization III

After running the game once and quitting, look in your gameDir for Civilization3.ini or conquests.ini (depending on the expansion/version you are using). Edit it, and add this line to the bottom:
keepRes=1

When you run the game, it should run at your desktop's resolution instead of 1024x768.

All of the game's various GUIs, dialogues, and interface windows have a fixed resolution, and scale correctly with the normal world map visible in the background. The only game element that does not work this way is the city screen. It is fixed at 1024x768, and if you run the game at a higher resolution, it is windowboxed.