Turning off Vertical Synchronization will not hurt the card. It is merely there (as theviper said) to lock the output of the card with the refresh rate of the monitor. That way, when the monitor refreshes it is not displaying half of the previous frame along with half of the next frame. It will always slow your FPS down to the next refresh rate point.
For example, if the card can do 200FPS, it will cap it at 60 to avoid "tearing" (mixing frames). If it can do 59FPS, it will cap it at the next refresh rate down, say 30FPS (or Hz) to stop the monitor from displaying mixed frames. So, if you are running in the 60+FPS range, it is best to turn it on. Below that it should be based on what looks best to you. You'll lose FPS with it on, but if it looks terrible, it is probably better to leave it on regardless.
Anyway, none of the four settings should be able to damage the card.