Wanted to pop in and say I'm having the same issue with my Alienware M11x r2 (which runs the GeForce 335M). Sometimes, the game will just crash with a generic "Final Fantasy XIV has stopped working" dialog box or the game will freeze and then my display will crash saying the DirectX device recovered. I don't have any issues on any other games.
Having just started, I'm hesitant to join a party due to how random and frequent these crashes seem to be. The 300.83 driver doesn't support my card, so I can't go that route, and the 304.48 driver didn't fix a thing for me.
After looking in the Event Viewer logs, sometimes the faulting module will be ffxivgame.exe and other times it will be d3d9.dll version 6.1.7601.17514. Honestly, the only reason I continue to pay for this game is the hope that 2.0 will be better. It might be stupid to place my trust in SE like that, but I'm really looking forward to playing.