If someone got drugged at a party, and had no recollection of what they did including hitting a car and still driving until they got pulled over, what would happen?

IF they can prove that they were drugged without their knowledge or consent, they would likely have a good defense to criminal liability (e.g. for DUI or leaving the scene of an accident) and *may* have a good defense to civil liability (e.g. a lawsuit)--the issue with civil liability is that

1) the standard  of proof is lower, making it easier to win a lawsuit then get a criminal conviction; and

2) it's enough to be civilly liable (i.e. be found to owe money for property damage or injury) that the person was "negligent," or careless; it may be, for example, that driving to a party where, at a minimum, alcohol was going to be served means that the person was careless about the possibility of becoming intoxicated in one way or another, and so could be considered to have been negligent. (Or alternately, if there was *any* reason for the person to think he/she may have been impaired, then getting behind the wheel would be negligent.)

So while the person might be able to avoid having to pay for any damages or injuries, his/her defense to a lawsuit is not as strong as his/her defense to criminal liability and there's a not-insigificant chance of civil liability.

The person could obviously sue--and press charges against--the person who drugged him/her, if that person could be identified.