I am having an identical problem; periodically the game will freeze (actually, the machine locks up).
It had happened only after I hit 'Turn', but then last night it happened once after I hit 'Done' ('Close'? I can't remember) on a planet window.
All three times were hard freezes that required cycling the machine.
I run ME, P3-933, plenty of disk space available, 512MB ram, ATI 9000 Pro with latest drivers, on-board SB.... not sure what other info to provide.
Frankly, I don't expect you to be able to track this down from that limited information.
But if you could suggest a method to help provide you with useful info, Frogboy, I'd be all over it. It doesn't seem to happen at 'the same place'. For instance, after rebooting, I'll load up the latest auto-save and it'll work just fine past wherever the last crash was.
Regardless, I love this game. I'd love to get this problem fixed, but either way -- very nice job.
(Cari said to send her autosaves and whatnot. When it happens again tonight I will do that.)
Pooks