The answer is, as always, that it depends.
Let's take a quick look at what those three numbers mean. The first number is the "per-person" personal injury liability amount. If you ran a red light tomorrow and T-boned another car, the insurance company would pay damages up to this amount to each person in the other car that was injured in the accident. What the actual damages would be depends on the severity of the accident and how many people were in the other car; remember that "personal injury damages" include not only the actual medical bills incurred to treat the immediate injury, but lost time, compensation for any long-term or permanent disability, pain and suffering, etc.
The second number is the "per-incident" personal liability amount. This limit provides a second level of upper limit; regardless of how many people were hurt and how much they come after you for, the insurance company will cover an overall maximum of this second amount in personal injury claims arising from a single accident. Again, damages awarded go beyond medical bills incurred.
The last number is the "property damage" liability amount. This is the money that pays to fix or replace the other person's car, repair or rebuild the wall or window you plowed through, repair or replace anything inside the car or on the other side of the wall that you damaged/destroyed, etc. Basically if it doesn't have a birth certificate, any damage you deal to it in the accident falls under this last number.
Given what each of those numbers represents, you must now make a decision. How much damage can you do in the average accident, and how able are you to cover anything that your insurance won't? The answers, for the majority of us, are "a lot" and "not at all" respectively.
Simple example: You run that red light and plow into another guy on his way to work in a 5-year-old Toyota Camry. He ends up injured badly enough to go to the hospital, and the car's totalled. The average hospital stay is about $33,100 according to a number I grabbed off Google. Add to that a month off the job at $4,500 gross monthly pay, a $500 ambulance ride, and some reasonable pain and suffering (say $5,000), but luckily he makes a full recovery with no long-term effects. You and your insurer are jointly on the hook for $43,100 in personal liability, plus the blue book value of the Camry as it was before the crash; say $15,000. Your insurer will stand between you and the other guy and hand him the check for both the personal injury and for the car. This happens every day, and while it's a huge inconvenience for a lot of people, after a few years things get back to normal for all involved.
Different example: You run the same red light and plow into the same Camry, but now the guy has his family with him; 3 more bodies in the car. You send all four of them to the hospital. The car, again, is totaled, but now that's the least of your worries; you now have four hospital stays at 30 large apiece, double the time off work for the man and his wife (two-income family), and quadruple the pain and suffering. For pretty much the same incident, just because there was more than one other person in that car, you are now liable
for $162,200. Your 50/100/50 insurance policy only covers $100,000; you now have to make some sort of agreeable arrangement to pay them $62,200. If they aren't interested in a structured payment settlement, they can take your house, your retirement, your kid's college funds, anything of value that you have equity in. This is way beyond "inconvenient"; it could mean you owe someone else every spare penny a judge thinks you have for the rest of your life. If instead you paid a little more for a 100/300/100 policy, your insurer would have written the whole check.
Another different example; same red light, same you running it, only one guy in the other car... which is now a brand-new $80,000 BMW 6-series. Just to spice things up, he had a $3000 laptop in his briefcase on what used to be the passenger seat, that's now a crumpled hunk of metal and silicon. He's fine, thank God, but seriously cheesed off that his laptop and his midlife crisis are total losses. Your 50/100/50 plan? Leaves you on the hook for $33k in property damages. A 100/300/100 plan would have covered it in full (albeit probably putting you on public transit or a van pool for the next 3 years; a driver who totals a car worth more than 50 large is automatically put in the highest-risk pool of covered drivers).
So, to answer the question, look around. See the other cars around you on the road on your next commute. What is the average blue book value of those cars? How many people, on average, are in each one? You pretty much need insurance sufficient to ensure you can walk away from an accident not owing a penny for any level of damages you may incur that don't result in permanent disability or death.
Insurance for death and disability is not the kind of thing the average person can even afford; the average judgement for wrongful death is $2.9 million according to another number I pulled off Google. To be fair, that figure probably has a lot of medical malpractice - translated: deep pockets - figured into it, but wrongful death judgments in general are some of the most expensive you'll ever see. Consider future earnings potential alone; if you make the median $55,000, and you're 30 and plan to retire at 65, you would expect to bring home $1.925 million in that time. If someone accidentally killed you tomorrow, that's the least your family could expect to get in a judgement; it would be easy to argue for about another million more in retirement savings (which is your $2.9m right there). On top of that, there are less significant but still individually-insurmountable damages for loss of companionship, bereavement, medical expenses (they still send you a bill if you die), funeral expenses, your pain and suffering (if you weren't instantly killed) and punitive damages (if the death was considered a direct result of "willful disregard for human life"; basically if the circumstances were so preventable it took effort not to prevent them).
