The amount of money a successful plaintiff receives in a personal injury lawsuit is often referred to as "damages." In most states, and in most kinds of personal injury cases, a jury is usually free to award whatever amount they think appropriate. But statutory limits on damages will apply in certain cases.
The first thing to understand is the two most common categories of damages in a personal injury case: economic and non-ecomonic.
"Economic damages" are concrete damages that the injured person (the plaintiff) or the plaintiff's insurance company has paid out and/or will continue to pay out as a result of the injury—medical bills, for example. Economic damages also include concrete amounts the plaintiff has missed out on and/or will continue to miss out on, like lost income.
"Non-economic damages" include most other categories of harm and negative effects of the underlying accident, most importantly the various types of "pain and suffering" and "loss of enjoyment of life" experienced by the plaintiff. Unlike economic damages, a jury does not base a plaintiff's non-economic damage awards on past losses and future calculations; it must make a more subjective evaluation.
While no state currently has a cap in place on economic damages across all kinds of personal injury cases, a handful of states have capped non-economic damages in most injury-related cases (whether arising from a car accident, a slip and fall, or any other kinds of mishap).
A number of states (about half) have also capped non-economic damages in medical malpractice cases. The cap amounts (i.e. the maximum amount of non-economic damages a successful medical malpractice plaintiff can recover) vary. In California, the cap is $250,000. It's important to note that a number of exceptions either permit a higher damage cap or eliminate the cap altogether in certain kinds of cases.
A small number of states have also capped non-economic damages in product liability cases, but again, exceptions will apply.
Rare in personal injury cases, punitive damages are designed to punish intentional wrongdoing and deter future bad conduct. They're usually assessed based on the defendant's wealth. A 2005 U.S. Supreme Court decision set guidelines to prevent excessive punitive damage awards, and a number of states have enacted laws that limit punitive damage awards in personal injury claims, or eliminate them altogether. Some have fixed caps and others have a fixed multiplier based on other damages in the case. For example, a punitive damages cap law might require that punitive damages be no higher than three times the plaintiff's economic and non-economic damages.
States have also made other changes to traditional rules in the name of tort reform. The first is a change to the traditional rule of "joint and several liability." Under the traditional rule, a plaintiff could collect the full amount of damages from one defendant, even though multiple defendants were at fault for the accident that led to the claim. The rationale for joint and several liability was that the plaintiff should not be punished simply because one of the defendants was broke or impossible to find; it was more fair for a partially at-fault defendant to pay more than her share of the liability to make the plaintiff whole. A number of states have passed laws eliminating joint and several liability and now require a defendant to pay only his or her proportionate liability.
Next, the "collateral source rule" prevents the defendant from presenting at trial evidence that the plaintiff has received compensation for the injuries from another source, for example from his or her medical insurance. The rationale behind this rule was that the jury would reduce the plaintiff's damages if they heard about the other compensation, and that most insurers would collect from the plaintiff's damage award what they had paid out (via a personal injury lien). To treat the situation otherwise would give the defendant a windfall, despite being liable, and punish the plaintiff and/or the insurance company (an insurance company will typically have a lien on any amount the plaintiff is awarded up to the amount the insurance company paid out).
Many states have modified the collateral source, predominantly in medical malpractice actions, but also in general civil liability cases like personal injury. Most of the modifications provide that the rule is still in place if a medical insurance lien (called a "subrogation right") is involved, but some do not. As with some state damage caps, a number of the collateral source rule statutes have been ruled unconstitutional by state courts.