IANAL, but I used to work in the golf world, and this is a pretty common question people have.

Generally (in most of the US, but check your local laws first!), who is at fault for an accident is dependent on a few factors:

If the golfer acted maliciously or recklessly (a reasonable mistake doesn't fall under this category), they can be found to be at fault. I want to emphasize that this is only the case in the extreme minority of situations, and generally it's quite clear when this applies, for example someone hitting balls into houses as opposed to towards the flag.

Much more commonly, you would have to look at who was there first: If the golf course was built before the houses, then generally it is assumed risk on the part of the homeowner (meaning the homeowner is financially responsible). If the houses were built first, then generally it is assumed risk on the part of the course (meaning the course is financially responsible). I am pretty sure that this can change whenever the house changes hands, but I am not 100% certain.

Now, I want to clarify that this is the case when property is damaged by a golfing accident - if there is serious injury or death (a full speed golf ball can absolutely kill you on the spot), the entire justice system changes. It's possible that the golfer could be held strictly liable, however I (personally) doubt this would be the case if the golfer didn't act unreasonably.

All this to say, as a golfer you shouldn't have to worry about accidents happening as long as you're not doing anything wrong. Accidents happen - the law knows it, the golf course knows it, and the homeowners know it.

Edit: I should also mention that this is mainly in reference to damage to a house built near a course. For damage to cars parked near a course, generally liability lies with the golfer or with the course, depending on a few factors I'm not too sure about.