What you are asking about is hazard assessment. The first thing a tree needs to be considered a hazard, is a target. What will the tree hit if it fails?
Next, it needs some kind of fault or weakness.
If you have an arborist come to look at your trees, he should be able to walk around and assess the trees. If you are going to hire the tree work out, most arborist will do this type of walk around as a free estimate, in the hopes he'll get the work, otherwise there may be a consulting fee.
If you are concerned about liability for the damage to you r neighbor's car, unless the neighbor advised you of a problem with the tree before it failed, his insurance will take care of the damages and that will be that. If your trees are in horrible shape and are obviously hazardous, that might be different, which is why having a proffesional come in to look things over from time to time may be a good idea.
He'll look for dead or dying limbs, weak crotches, hollows, cracks, root damage, buried root flares, disease, low vitality, and anything else that might be a problem.
He will likely recommend a crown cleaning on the higher value trees, to remove hazards, deadwood, badly crossing limbs and do a more complete inspection. This type of work can get expensive, so what most folks do is set a budget for tree maintenance and have an arborist come in for some set amount of time each year, to take care of the most important things.
Older trees can become hazardous and seem like a liability, but if they are given at least some maintenance, they become a big asset, both in terms of property value and value to society.
Be carefull in hiring. Look for an ISA certified arborist, make sure he gives you proof of insurance (including Workmans compinsation) in writting from the insurance compay before work starts, and don't let him climb your trees with spikes on his feet, unless he's removing it. You'll want to ask him if he follows ANSI standards and wears safety gear like hardhat, safety glasses, and cut resistant chaps. Be leary of somebody that wants to remove lower limbs for no reason, this often indicates an unskilled arborist looking for the easiest work, and can be very bad for the tree. The same is true for gutting the tree (removing small interior shoots and limbs).
Asking these things will help insure your getting somebody that will do good things to your trees, and not permenently damage your valuable assets. Unfortunately, the tree service industry has many unqualified "hacks", that you wouldn't want working in your yard, even if it were for free. The interview at the estimate is your best protection.