If you win a lawsuit, you may be entitled to a sum of money, known in the legal world as "damages." Damages, in many cases, come in two major categories: punitive and compensatory damages. Punitive damages seek to punish the person for their wrongdoing. In contrast, compensatory damages are intended simply to pay the person who was injured.
The answer is: nearly anything. If the person who brought the lawsuit (known as the "plaintiff") was physically injured, compensatory damages could include his medical bills, the pay he missed from taking too many sick days, and pay he will lose in the future from a reduced capacity to work. Also, many courts will consider many different types of injuries. For example, if the plaintiff was badly frightened and suffered nightmares, increased blood pressure, or other anxiety related symptoms which prevented him from working or fully enjoying his life, he could seek damages for "emotional distress." If any of his property was damaged, compensatory damages could also include the cost of any repairs, or the value of any property that was destroyed.
It's worth noting that the amount of compensatory damages a plaintiff can seek depends on the kind of case the plaintiff brings. To show the difference, take a look at two famous textbook cases about damages, one in personal injury, and one in contracts.
Case 1: Playground Games Gone Wrong
A boy in nineteenth century Wisconsin injured his knee. Sometime later, he was in school and a classmate kicked that same knee. The kick was so light the boy did not feel any pain at first, but later on the knee became infected, and the boy was never able to use his leg again. He sued his classmate. The court found that the classmate was at fault and had to compensate the boy for the loss of his leg, even though the classmate could not have known that his kick would have such extreme consequences.
Case 2: The Case of the Cracked Crankshaft
A mill owner in nineteenth century England discovered that part of his mill, the crankshaft, was broken. The miller hired someone else, a carrier, to bring the crankshaft to Greenwich for repair. The carrier did not deliver the crankshaft on time, and returned it to the miller much later than expected. The carrier did not know, however, that the mill could not operate without the crankshaft, and that the miller lost a lot of money while the crankshaft was gone. The miller sued the carrier, but the court held that the carrier did not need to pay the miller for lost profits because the carrier did not know he could be responsible for these profits when he made the contract.
See FindLaw's section on Litigation for more information.
