I just got Civ4 yesterday. Installed and played without a hitch with the resolution at 1280x1024. I think I might go higher next time, just so I can see more of the world at any given time.
For me, the jury is still out on this one. It seems more RTS-like, rather than Civ-like. Maybe it'll grow on me, we'll see. That aside, the game has run flawlessly for a few hours without a hint of slowdown on my system.
CW