Once you’ve completed Kasumi’s loyalty mission – Stolen Memory, and gotten the mission rundown, your game may crash. This is what worked for me (Windows 7, 64 bit, Origin edition).

In Windows Explorer, navigate to the ME2 folder – the default is C:\Program Files (x86)\Origin Games\Mass Effect 2\ and go into the Binaries folder. There, make a shortcut to ME2Game.exe on the desktop and in the properties of that shortcut, add -nomoviestartup to the end of the Target section. Make you sure you put it outside the quotes.

Load the game and it should work. If not, try the above with MassEffect2.exe instead.

Edit: this fix works for the crash at the end of the Lair of the Shadow Broker mission too.

Thanks to the various posters here for the tips.