It depends on your assets. Do you have more than 500K that couldn't be protected in the event you were sued? State creditors can't each an IRA or 401K. Most states will allow judgment creditors to file a judgement lien against a homestead but won't let the creditor foreclose the lien on a personal residence. Business property should already be in a separate entity.
So lets say you have 350K of hard assets at risk. 500K is more than enough. In fact, 250K might be more than enough because a lawyer looking at policy limits (hard cash, or a "bird in hand)) versus the risk of trial for nothing more than the right to try to collect the additional 100K (a risky bet, or "two birds in the brush") is going to advise his client to take the policy limits.
If the plaintiff offers to settle for the policy limits (250K) but the insurer refuses to so, thereby exposing you to a potential higher award, then most states allow you to transfer your cause of action against the insurance company to the plaintiffif the jury awards an amount higher than your policy limits. This allows the plaintiff to recover the excess award from your insurance company.
The number one rule is don't over insure your liability - all you are doing is spending money for the benefit of the person you injure.
Instead, you should spend the extra insurance premium dollars on disability or accident insurance for yourself in case you are injured by someone with very little insurance or no insurance.