How likely is it that a virus will spread across the globe and create a worldwide epidemic within your litfetime?

Global viruses. Yes. Because of huge increases in the world populations, and the ease of travel among countries, a new virus or a mutated virus can infect huge numbers of people and be rapidly dispersed around the world and cause an epidemic before it is controlled and vaccines can be made up to give immunity.
Viral epidemic. There is no way to predict this accurately but I would say it is possible but not likely in my opinion.