I have been having lots of crashes with this game. I'm not sure if it's just my platform (XP 64-bit edition), or if it also happens in a 32-bit OS. Basically, the thing that kills me most often is the ship design and the invasion stuff.
When I design a new ship and click on something that puts the space available bar into the red, the design window locks up. I can hit next turn until the auto-save happens, but then I have to alt-tab and end-task, then load the autosave. I have a saved game where I just did this and now I cannot even open the saved game without a crash. Also, once the game crashes, I have to reboot to get back into it, so it seems like it is destabalizing the OS, which I have not had happen on me since I moved to XP.
Also, in the invasion battles, it will just randomly crash out. Again, I need to reboot to get back into the game.