Should there be limits to the amount of money that a successful plaintiff can be awarded at trial?
No, there should not be any limit on how much a jury can award a plaintiff at a civil trial. The reason for this is that it is impossible to know what amount is appropriate without reference to the terms of a case.
Punitive damages have to be punitive enough to deter the offender from reoffending. This means that they have to be able to change with the circumstances. For example, let us say that a large and very prosperous company engages in some sort of conduct that creates dangerous situations for its workers. It might lead to the serious injury of one or two workers a year, but it is very lucrative. Now let us imagine that the damages that can be imposed upon the company are limited. What if the damages are limited to $1 million, for example, and the conduct that causes the danger is worth $10 million per year to the company? The company would not have much incentive to rectify the situation.
Thus, there is not really any good way to limit damages that can be awarded to a successful plaintiff.