If we define "Manifest Destiny" in a broad sense, it clearly does still exist in the minds of many or most Americans today. In a broad sense, Manifest Destiny is the idea that the United States is somehow special and that it is destined to spread its culture and its governmental system across the world. It is hard to deny that we still feel this way.
In the 1800s, the term "Manifest Destiny" had a much more imperialistic flavor. We do not have that idea today. We no longer think that we would be justified in actually taking land from other countries in the way that we took much of Mexico in the 1840s. So, in that sense, Manifest Destiny does not still exist as a belief in our minds. We can see this in the fact that no one thinks that we should take Iraq or Afghanistan in the way we once felt justified in taking the Philippines.
On the other hand, we still do think that other countries ought to become more like us. We can see this in our dealings with Iraq and Afghanistan among many others. We do feel that it is our destiny and our duty to spread democracy across the world.