I have almost the exact same problem as eagleFMJ and DoomsWord89, only I appear to crash a little sooner, actually. In the first Crusader mission, I have just completed the first objective, (Secure the Port). Then I decide to go for the building site atop the huge hill overlooking the city. I move my units up and start fighting the defending Saracens. Then, in the middle of this battle, the game crashes and sends me to desktop.
FYI, I am using the GamersGate version and have the newest drivers for my graphics-card.