As an author one has two interests: That one's works should be widely enjoyed (i.e. the wish to leave a mark on the world, and be popular), and the wish to earn money. In the current system the latter is solved via copyright: Each author has a monopoly on distributing his works for a (very, very long) time, letting him sell copies of his work with little worry of competition. This mechanism works, but it is not optimal because it conflicts with the other goal of authors, which is that one's works should be widely enjoyed. Under copyright, income depends on strict control of copying, and unauthorized copying potentially represents lost sales. The author therefore finds himself trying to stop others from spreading his work, and to limit those who enjoy it to those who bought a copy. His first and second goals are working against each other.
In a perfect system, authors would not have such a conflict of interest with themselves. Several alternatives to copyright exist which solve this problem, but introduce others.
1. Upfront payment (Kickstarter): The author asks for the full payment for his work before he performs it, rather than extracting it gradually over years afterwards. This could be organized in the same manner as the highly successfull Kickstarter: They author creates a Kickstarter page detailing his plan for, say, a new book, with some information about what it would be about, and states a price he wants for writing it (say 50,000€), possibly with some stretch goals (bonus chapter after 100,000€, for example). Potential readers then choose how much money they want to commit. Once enough money to reach the author's price has been reached, he gets the money, and starts working. If too much time passes (time-limit is commonly 90 days with Kickstarter) without the goal being reached, then the potential readers get their money back, and the author must try some other approach.
The advantage of this approach is that since the author has already been paid before he does the work, he does not need to control copying: copies are free, and can be shared freely. The more copies are shared, and the more people who enjoy his work, the easier it will be for him to gather money for his work.
The disadvantage of this system is that it will be hard for unknown authors to find people willing to fund them. Probably, their first book would need to be written for free in order to get enough interested readers for this approach to work. On the other hand, in practice, authors already write their first book for free under the current system (they need something to show the editor in order to be funded), so this is not a serious disadvantage.
Projects of more than $1,000,000 are regularly funded through Kickstarter, and more than 50,000 projects have been funded during the 4 years since its founding. So a Kickstarter-inspired model of up-front payment really looks like it could work.
2. Usage-based payment: In stead of the author selling copies, the state could measure how much his works are used and compensate him accordingly. That would solve his conflict of interest with himself - now it would be in his economic interest to see people share his work with each other. Something similar to this has been in use for some artists in Norway since 1886, though in a much less expansive fashion. An advantage of this approach is that it allows one to make the economic reward non-proportional to the popularity. For example, one could reduce the money per fan per work for the most popular works in order to encourage diversity and avoid super-star effects where a few authors become billionaires while others get nothing (like the current system). A disadvantage of this is that it would require a significant bureaucracy, and there could be difficulties in getting unbiased measurements of popularity of individual works.
3. Donation-based payment: Fans of works could voluntarily donate money to authors. This would make the author's income grow as the number of fans grow, and it would be in authors' interest to let as many people enjoy their work as possible. However, the author's income would be unpredictable, and more so the less popular he is. Still, Wikipedia has proven that even a large project with significant hardware expenses can survive exclusively on donations.
These three suggestions are listed in the order of my preference, but they all have in common that they would make copyright unnecessary, and hence free up our culture, allowing anybody to distribute and modify what movies, book and songs they want, and saving society from the significant economic social cost of enforcing copyright.