It's still important for several reasons. It's a statement of who we are as Americans and defines the beliefs at the very foundation of our system of government. It announces to the world the principles by which we recognize the right of a people to overthrow their government (and the conditions under which it becomes the only other means of settling their disputes).
It also provides us, ourselves, a constant reminder of how to recognize when our own government has become tyrannical - meaning too powerful, arbitrary in the application of the law, and disdainful of the individual Liberty of each and every one of us.
It should also serve as a caution to our federal government that it risks its own survival when it usurps our rights.
But there are two kinds of people who would ask this question in the first place: the young, who are just learning American history and the workings of our Republic... and those who actively reject the view that individual Liberty is a noble goal worth preserving. Usually, they do this because they think the world is too complicated and too different after two hundred years for those ideas still to have any relevance. Or they might be too comfortable in the relative safety Americans have enjoyed...
When we ook at the dangers that exist in the world, and when we have absolute trust in the federal government, it's easy to allow it to exercise more and more control over our lives. We can be free, or we can be safe. But we can't be both. As you continue your exploration of this question, keep asking yourself which is more important to you.