The title of the video below suggests the interview with Richard Dawkins and Lawrence Krauss is about the movie Unbelievers and atheism, but in fact the discussion is mostly about science and what it means to them.
Starting at 24:38 the interviewer asks whether they really meant to suggest that science can be spiritual? In their answers they confirm that they do in a non supernatural way and talk about their personal spiritual experiences in the sense Carl Sagan used the word.
I too have had such experiences when I first saw Saturn's rings through a telescope and when I visited CERN and realized the engineers managed to create literally the coldest place in the known universe to make superconducting possible.
For me the experience doesn't have to be special 'doing something for the first time' event. I frequently have such spiritual experiences in mundane situations too. For example, recently I watched the snow falling and I imagined how each snow crystal takes up a unique shape despite the simple rules of crystallization. Another time I was looking at a crowd of people and I thought about how we're all related as one human family descending from a single tribe.
I love science because it indeed makes living life a deeper experience. Knowledge doesn't take away from the wonder at all, quite the opposite.
The same applies to culture in general. For instance, when I visit a place and I know about its history the sightseeing becomes a much richer and more enjoyable.
If you have had any such experiences, do share.